{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/11.jpg' \/><\/center>H\u00ecnh ch\u00f3p \u0111\u1ec1u c\u00f3 m\u1eb7t b\u00ean l\u00e0 c\u00e1c ________ v\u00e0 \u0111\u00e1y l\u00e0 ________","select":["A. tam gi\u00e1c vu\u00f4ng b\u1eb1ng nhau c\u00f3 chung \u0111\u1ec9nh; t\u1ee9 gi\u00e1c","B. tam gi\u00e1c c\u00e2n b\u1eb1ng nhau c\u00f3 chung \u0111\u1ec9nh; tam gi\u00e1c","C. tam gi\u00e1c c\u00e2n b\u1eb1ng nhau c\u00f3 chung \u0111\u1ec9nh; \u0111a gi\u00e1c \u0111\u1ec1u","D. tam gi\u00e1c vu\u00f4ng b\u1eb1ng nhau c\u00f3 chung \u0111\u1ec9nh; \u0111a gi\u00e1c \u0111\u1ec1u"],"hint":"Nh\u1edb l\u1ea1i \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u1ec1u","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.2.png' \/><\/center>H\u00ecnh ch\u00f3p \u0111\u1ec1u c\u00f3 m\u1eb7t b\u00ean l\u00e0 c\u00e1c <i>tam gi\u00e1c c\u00e2n c\u00f3 chung \u0111\u1ec9nh<\/i> v\u00e0 \u0111\u00e1y l\u00e0 <i>\u0111a gi\u00e1c \u0111\u1ec1u<\/i>.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":1}]}],"id_ques":1870},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/2.jpg' \/><\/center>H\u00ecnh ch\u00f3p c\u1ee5t \u0111\u1ec1u c\u00f3 m\u1eb7t b\u00ean l\u00e0 c\u00e1c ________v\u00e0 \u0111\u00e1y l\u00e0 ________","select":["A. h\u00ecnh thang; t\u1ee9 gi\u00e1c","B. h\u00ecnh thang c\u00e2n; tam gi\u00e1c","C. h\u00ecnh thang; \u0111a gi\u00e1c \u0111\u1ec1u","D. h\u00ecnh thang c\u00e2n; \u0111a gi\u00e1c \u0111\u1ec1u"],"hint":"Nh\u1edb l\u1ea1i \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t \u0111\u1ec1u","explain":" <span class='basic_left'>H\u00ecnh ch\u00f3p c\u1ee5t \u0111\u1ec1u c\u00f3 m\u1eb7t b\u00ean l\u00e0 <i>h\u00ecnh thang c\u00e2n<\/i> v\u00e0 \u0111\u00e1y l\u00e0 <i>\u0111a gi\u00e1c \u0111\u1ec1u<\/i>.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span><\/span>","column":2}]}],"id_ques":1871},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"],["6"],["7"],["7"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"H\u00ecnh ch\u00f3p c\u00f3 $6$ m\u1eb7t b\u00ean th\u00ec c\u00f3 _input_ c\u1ea1nh \u0111\u00e1y, _input_ c\u1ea1nh b\u00ean,_input_ m\u1eb7t v\u00e0 _input_ \u0111\u1ec9nh.","hint":"","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.3.png' \/><\/center>H\u00ecnh ch\u00f3p c\u00f3 $6$ m\u1eb7t b\u00ean th\u00ec c\u00f3 \u0111a gi\u00e1c \u1edf \u0111\u00e1y l\u00e0 l\u1ee5c gi\u00e1c.<br\/> Do v\u1eady, h\u00ecnh ch\u00f3p c\u00f3 $6$ c\u1ea1nh \u0111\u00e1y, $6$ c\u1ea1nh b\u00ean, $7$ m\u1eb7t (th\u00eam $1$ m\u1eb7t \u0111\u00e1y) v\u00e0 $7$ \u0111\u1ec9nh (th\u00eam m\u1ed9t \u0111\u1ec9nh \u1edf ch\u00f3p)<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 l\u1ea7n l\u01b0\u1ee3t ph\u1ea3i \u0111i\u1ec1n l\u00e0 $6;6;7;$ v\u00e0 $7$<\/span><\/span>"}]}],"id_ques":1872},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"],["15"],["7"],["10"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"H\u00ecnh ch\u00f3p c\u1ee5t c\u00f3 $5$ c\u1ea1nh \u1edf \u0111\u00e1y th\u00ec c\u00f3 _input_ m\u1eb7t b\u00ean, _input_ c\u1ea1nh,_input_ m\u1eb7t v\u00e0 _input_ \u0111\u1ec9nh.","hint":"","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.4.png' \/><\/center>H\u00ecnh ch\u00f3p c\u00f3 $5$ c\u1ea1nh \u1edf \u0111\u00e1y th\u00ec c\u00f3 \u0111a gi\u00e1c \u1edf \u0111\u00e1y l\u00e0 ng\u0169 gi\u00e1c.<br\/> Do v\u1eady, h\u00ecnh ch\u00f3p c\u00f3 $5$ m\u1eb7t b\u00ean, $15$ c\u1ea1nh ($10$ c\u1ea1nh \u1edf \u0111\u00e1y v\u00e0 $5$ c\u1ea1nh b\u00ean), $7$ m\u1eb7t ($5$ m\u1eb7t b\u00ean v\u00e0 $2$ m\u1eb7t \u0111\u00e1y) v\u00e0 $10$ \u0111\u1ec9nh (hai \u0111\u00e1y m\u1ed7i \u0111\u00e1y $5$ \u0111\u1ec9nh)<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 l\u1ea7n l\u01b0\u1ee3t ph\u1ea3i \u0111i\u1ec1n l\u00e0 $5;15;7;$ v\u00e0 $10$<\/span><\/span>"}]}],"id_ques":1873},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["SH","HS"],["SO","OS"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"<span class='basic_left'>Cho h\u00ecnh ch\u00f3p \u0111\u1ec1u nh\u01b0 h\u00ecnh v\u1ebd:<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.1.png' \/><\/center><br\/>Trung \u0111o\u1ea1n c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0 _input_<br\/>\u0110\u01b0\u1eddng cao c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0 _input_<\/span>","hint":"","explain":"<span class='basic_left'>Trung \u0111o\u1ea1n l\u00e0 \u0111\u01b0\u1eddng cao h\u1ea1 t\u1eeb \u0111\u00ecnh $S$ c\u1ee7a m\u1ed7i m\u1eb7t b\u00ean c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u1ec1u. Do v\u1eady, trung \u0111o\u1ea1n c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0 $SH$<br\/>\u0110\u01b0\u1eddng cao c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0 \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y, l\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i t\u1eeb \u0111\u1ec9nh \u0111\u1ebfn t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua c\u00e1c \u0111\u1ec9nh c\u1ee7a \u0111a gi\u00e1c \u0111\u00e1y.<br\/>Do v\u1eady, \u0111\u01b0\u1eddng cao c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0 $SO$<br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $SH$ v\u00e0 $SO$<\/span><\/span>"}]}],"id_ques":1874},{"time":24,"part":[{"title":"Ch\u1ecdn <u>nh\u1eefng<\/u> \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"Ch\u1ecdn \u0111\u01b0\u1ee3c nhi\u1ec1u \u0111\u00e1p \u00e1n","temp":"checkbox","correct":[["1","4"]],"list":[{"point":5,"img":"","ques":"Trong c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau, kh\u1eb3ng \u0111\u1ecbnh n\u00e0o <b>\u0111\u00fang<\/b>?","hint":"","column":1,"number_true":2,"select":["A. H\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c \u0111\u1ec1u","B. H\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh thoi","C. H\u00ecnh ch\u00f3p ng\u0169 gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 ng\u0169 gi\u00e1c","D. H\u00ecnh ch\u00f3p l\u1ee5c gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 l\u1ee5c gi\u00e1c \u0111\u1ec1u."],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.2.png' \/><\/center>A. \u0110\u00fang v\u00ec h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c \u0111\u1ec1u<br\/>B. Sai v\u00ec h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng<br\/>C. Sai v\u00ec H\u00ecnh ch\u00f3p ng\u0169 gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 ng\u0169 gi\u00e1c \u0111\u1ec1u<br\/>D. \u0110\u00fang v\u00ec h\u00ecnh ch\u00f3p l\u1ee5c gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 l\u1ee5c gi\u00e1c \u0111\u1ec1u.<br\/><span class='basic_pink'>V\u1eady c\u00e1c kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang l\u00e0 $B$ v\u00e0 $D$<br\/><span class='basic_green'>L\u01b0u \u00fd: <\/span> Khi v\u1ebd h\u00ecnh ch\u00f3p \u0111\u1ec1u trong kh\u00f4ng gian, h\u00ecnh vu\u00f4ng v\u1ebd nh\u01b0 h\u00ecnh b\u00ecnh h\u00e0nh, c\u00e1c tam gi\u00e1c \u0111\u1ec1u v\u1ebd nh\u01b0 tam gi\u00e1c th\u01b0\u1eddng.<\/span>"}]}],"id_ques":1875},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["35"],["17"],["6"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"Cho c\u00e1c h\u00ecnh ch\u00f3p t\u1ee9 di\u1ec7n \u0111\u1ec1u v\u1edbi k\u00edch th\u01b0\u1edbc nh\u01b0 h\u00ecnh v\u1ebd v\u00e0 trong b\u1ea3ng b\u1ea3ng. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.5.png' \/><\/center>Ho\u00e0n thi\u1ec7n b\u1ea3ng sau:<br\/><table><tr><th><\/th><th>H\u00ecnh 1<\/th><th>H\u00ecnh 2<\/th><th>H\u00ecnh 3<\/th><\/tr><tr><td>Chi\u1ec1u cao (h)<\/td><td>$4$<\/td><td>_input_<\/td><td>$15$<\/td><\/tr><tr><td>Trung \u0111o\u1ea1n (d)<\/td><td>$5$<\/td><td>$37$<\/td><td>_input_<\/td><\/tr><tr><td>C\u1ea1nh \u0111\u00e1y(a)<\/td><td>_input_<\/td><td>$24$<\/td><td>$16$<\/td><\/tr><\/table>","hint":"S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago.","explain":"<span class='basic_left'><b>Nh\u1eadn x\u00e9t:<\/b> <br\/>- V\u00ec $S.ABCD$ l\u00e0 ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u n\u00ean $ABCD$ l\u00e0 h\u00ecnh vu\u00f4ng v\u00e0 c\u00e1c m\u1eb7t b\u00ean l\u00e0 c\u00e1c tam gi\u00e1c c\u00e2n.<br\/>+) $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$<br\/>+) $O$ giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng ch\u00e9o.<br\/>- V\u00ec $SO$ l\u00e0 \u0111\u01b0\u1eddng cao n\u00ean $SO \\bot mp(ABCD) \\,\\Rightarrow SO\\bot HO$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.5a.png' \/><\/center><br\/><span class='basic_green'>H\u00ecnh 1:<\/span><br\/>X\u00e9t tam gi\u00e1c $SHO$ vu\u00f4ng t\u1ea1i $O$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$SO^2+OH^2=SH^2\\\\ \\Rightarrow OH^2=5^2-4^2\\\\ \\Leftrightarrow OH^2=9\\\\ \\Leftrightarrow OH=3$<br\/> Ta c\u00f3, $HA=HB;\\,OA=OC$, suy ra $HO$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c $ABC$.<br\/>Do \u0111\u00f3 $BC=2HO=6$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.5b.png' \/><\/center><br\/><span class='basic_green'>H\u00ecnh 2:<\/span><br\/>Ta c\u00f3, $HA=HB;\\,OA=OC$, suy ra $HO$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c $ABC$.<br\/>Do \u0111\u00f3 $OH=\\dfrac{1}{2}BC=12$<br\/>X\u00e9t tam gi\u00e1c $SHO$ vu\u00f4ng t\u1ea1i $O$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$SO^2+OH^2=SH^2\\\\ \\Rightarrow SO^2=37^2-12^2\\\\ \\Leftrightarrow OH^2=1225\\\\ \\Leftrightarrow OH=35$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.5c.png' \/><\/center><br\/><span class='basic_green'>H\u00ecnh 3:<\/span><br\/>Ta c\u00f3, $HA=HB;\\,OA=OC$, suy ra $HO$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c $ABC$.<br\/>Do \u0111\u00f3 $OH=\\dfrac{1}{2}BC=8$<br\/>X\u00e9t tam gi\u00e1c $SHO$ vu\u00f4ng t\u1ea1i $O$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$SO^2+OH^2=SH^2\\\\ \\Rightarrow SH^2=15^2+8^2\\\\ \\Leftrightarrow SH^2=289\\\\ \\Leftrightarrow SH=17$ <br\/><span class='basic_green'>Ghi nh\u1edb:<\/span> Trong h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 chi\u1ec1u cao (h), trung \u0111o\u1ea1n (d) v\u00e0 c\u1ea1nh \u0111\u00e1y (a) th\u00ec ta c\u00f3 bi\u1ec3u th\u1ee9c li\u00ean h\u1ec7: $h^2+\\left(\\dfrac{a}{2}\\right)^2=d^2$<\/span>"}]}],"id_ques":1876},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/16.jpg' \/><\/center>Cho h\u00ecnh ch\u00f3p \u0111\u1ec1u c\u00f3 chu vi \u0111\u00e1y l\u00e0 $120$ $cm$, \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung \u0111o\u1ea1n l\u00e0 $15$ $cm$. Di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0:","select":["A. $900\\,cm^2$","B. $1800\\,cm^2$","C. $3600\\,cm^2$"],"hint":"","explain":"<span class='basic_left'>Di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p b\u1eb1ng t\u00edch n\u1eeda chu vi \u0111\u00e1y v\u00e0 trung \u0111o\u1ea1n.<br\/>Ta c\u00f3 n\u1eeda chu vi \u0111\u00e1y l\u00e0 $120:2=60\\,(cm)$<br\/>Di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0 $60.15=900\\,(cm^2)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><br\/><span class='basic_green'>Ghi nh\u1edb:<\/span>H\u00ecnh ch\u00f3p c\u00f3 n\u1eeda chu vi \u0111\u00e1y l\u00e0 $p$ (\u0111\u01a1n v\u1ecb \u0111\u1ed9 d\u00e0i), \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung \u0111o\u1ea1n l\u00e0 $d$ (\u0111\u01a1n v\u1ecb \u0111\u1ed9 d\u00e0i). Di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u01b0\u1ee3c t\u00ednh b\u1edfi c\u00f4ng th\u1ee9c $S_{xq}= p.d$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)<\/span><\/span> ","column":3}]}],"id_ques":1877},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/10.jpg' \/><\/center>Cho h\u00ecnh ch\u00f3p ng\u0169 gi\u00e1c \u0111\u1ec1u. \u0110\u00e1y l\u00e0 ng\u0169 gi\u00e1c \u0111\u1ec1u c\u00f3 c\u1ea1nh d\u00e0i $10\\,cm$. \u0110\u1ed9 d\u00e0i c\u1ea1nh b\u00ean l\u00e0 $13$ $cm$. Di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0:","select":["A. $100\\,cm^2$","B. $150\\,cm^2$","C. $300\\,cm^2$","D. $600\\,cm^2$"],"hint":"T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y.","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.17.png' \/><\/center>X\u00e9t h\u00ecnh ch\u00f3p ng\u0169 gi\u00e1c \u0111\u1ec1u $S.ABCDE$ c\u00f3 $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ nh\u01b0 h\u00ecnh v\u1ebd.<br\/>G\u1ecdi \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y l\u00e0 $a\\,(cm,\\,a>0)$<br\/>Ta c\u00f3, tam gi\u00e1c $SAB$ c\u00e2n t\u1ea1i $S$ n\u00ean $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ea1nh $AB$<br\/>Suy ra, $SH\\bot AB$.<br\/>X\u00e9t tam gi\u00e1c $SAH$ vu\u00f4ng t\u1ea1i $H$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3: <br\/>$AH^2+SH^2=SA^2\\\\ \\Rightarrow 5^2+SH^2=13^2\\\\ \\Leftrightarrow SH^2=144\\\\ \\Leftrightarrow SH=12\\,(cm)$<br\/>Chu vi \u0111\u00e1y $ABCDE$ l\u00e0 $10.5=50\\,(cm)$<br\/>V\u1eady di\u1ec7n t\u00edch xung quanh h\u00ecnh ch\u00f3p $S.ABCDE$ l\u00e0 $12.\\dfrac{50}{2}=300\\,(cm^2)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span> ","column":4}]}],"id_ques":1878},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/8.jpg' \/><\/center>Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u. \u0110\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng c\u00f3 \u0111\u01b0\u1eddng ch\u00e9o d\u00e0i $12\\sqrt{2}\\,cm$. \u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung \u0111o\u1ea1n l\u00e0 $15$ $cm$. Di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0:","select":["A. $160\\,cm^2$","B. $360\\,cm^2$","C. $640\\,cm^2$","D. $2160\\,cm^2$"],"hint":"T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y.","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.16.png' \/><\/center>G\u1ecdi \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y l\u00e0 $a\\,(cm,\\,a>0)$<br\/>X\u00e9t tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $B$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3: <br\/>$AB^2+BC^2=AC^2\\\\ \\Rightarrow a^2+a^2=(12\\sqrt{2})^2\\\\ \\Leftrightarrow a^2=144\\\\ \\Leftrightarrow a=12\\,(cm)$<br\/>V\u1eady chu vi \u0111\u00e1y $ABCD$ l\u00e0 $12.4=48\\,(cm)$<br\/>V\u1eady di\u1ec7n t\u00edch xung quanh h\u00ecnh ch\u00f3p $S.ABCD$ l\u00e0 $15.\\dfrac{48}{2}=360\\,(cm^2)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span> ","column":4}]}],"id_ques":1879},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>Cho h\u00ecnh ch\u00f3p c\u1ee5t t\u1ee9 gi\u00e1c \u0111\u1ec1u $ABCD.A\u2019B\u2019C\u2019D\u2019$ c\u00f3 \u0111\u1ed9 d\u00e0i c\u1ea1nh b\u00ean l\u00e0 $a\\sqrt{5}$, \u0111\u01b0\u1eddng cao c\u1ee7a m\u1eb7t b\u00ean l\u00e0 $2a$ v\u00e0 c\u1ea1nh \u0111\u00e1y b\u1eb1ng $3a$. <br\/><b>C\u00e2u 1: <\/b >T\u00ednh di\u1ec7n t\u00edch m\u1eb7t b\u00ean c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.10.png' \/><\/center><\/span>","select":["A. $2a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)","B. $3a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)","C. $4a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)","D. $8a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)"],"hint":"M\u1ed7i m\u1eb7t b\u00ean l\u00e0 m\u1ed9t h\u00ecnh thang c\u00e2n","explain":" <span class='basic_left'>X\u00e9t m\u1eb7t b\u00ean $AA'B'B$ l\u00e0 h\u00ecnh thang c\u00e2n c\u00f3 chi\u1ec1u cao $A'H=2a$<br\/>X\u00e9t tam gi\u00e1c $AA'H$ vu\u00f4ng t\u1ea1i $H$.<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3: <br\/>$AA'^2=AH^2+A'H^2\\\\ \\Leftrightarrow AH^2=AA'^2-A'H^2\\\\ \\Rightarrow AH^2=5a^2-4a^2 \\\\ \\Leftrightarrow AH^2=a^2\\\\ \\Leftrightarrow AH=a$<br\/>D\u1ef1ng \u0111\u01b0\u1eddng cao $B'K$.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.10a.png' \/><\/center><br\/> V\u00ec $AA'B'B$ l\u00e0 h\u00ecnh thang c\u00e2n n\u00ean ta d\u1ec5 d\u00e0ng ch\u1ee9ng minh \u0111\u01b0\u1ee3c $\\Delta AHA'=\\Delta BKB' \\Rightarrow AH=KB=a$ v\u00e0 $A'HKB'$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt n\u00ean $A'B'=HK=a$<br\/>V\u1eady di\u1ec7n t\u00edch m\u1eb7t b\u00ean $AA'B'B$ l\u00e0 $\\dfrac{1}{2}(A'B'+AB).A'H=\\dfrac{1}{2}.(a+3a).2a=4a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":1880},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>Cho h\u00ecnh ch\u00f3p c\u1ee5t t\u1ee9 gi\u00e1c \u0111\u1ec1u $ABCD.A\u2019B\u2019C\u2019D\u2019$ c\u00f3 \u0111\u01b0\u1eddng cao c\u1ee7a m\u1eb7t b\u00ean l\u00e0 $2a$ v\u00e0 c\u1ea1nh \u0111\u00e1y b\u1eb1ng $3a$. <br\/><b>C\u00e2u 2: <\/b >T\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.10.png' \/><\/center><\/span>","select":["A. $16a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)","B. $26a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)","C. $32a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)","D. $42a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)"],"hint":"Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n b\u1eb1ng t\u1ed5ng di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch hai \u0111\u00e1y.","explain":" <span class='basic_left'>Theo c\u00e2u 1, ta c\u00f3: Di\u1ec7n t\u00edch xung quanh h\u00ecnh ch\u00f3p c\u1ee5t $A'B'C'D'.ABCD$ l\u00e0 $4.4a^2=16a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)<br\/>\u0110\u00e1y $A'B'C'D'$ l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh $a$ (\u0111\u01a1n v\u1ecb \u0111\u1ed9 d\u00e0i) n\u00ean c\u00f3 di\u1ec7n t\u00edch l\u00e0 $a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)<br\/>\u0110\u00e1y $ABCD$ l\u00e0 h\u00ecnh vu\u00f4ng c\u00f3 c\u1ea1nh $3a$ (\u0111\u01a1n v\u1ecb \u0111\u1ed9 d\u00e0i) n\u00ean c\u00f3 di\u1ec7n t\u00edch l\u00e0 $(3a)^2=9a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)<br\/>V\u1eady di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t $ABCD.A'B'C'D'$ l\u00e0 $16a^2+a^2+9a^2=26a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)<br\/>Ngo\u00e0i c\u00e1ch gi\u1ea3i tr\u00ean, b\u00e0i to\u00e1n c\u00f3 th\u1ec3 th\u1ef1c hi\u1ec7n b\u1eb1ng c\u00e1ch \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c:<br\/> $S_{xq}=(p+p').d$<br\/>$S_{tp}=S_{xq}+S_1+S_2$<br\/>(trong \u0111\u00f3: $p;p'$ l\u00e0 n\u1eeda chu vi \u0111\u00e1y l\u1edbn v\u00e0 \u0111\u00e1y nh\u1ecf; $d$ l\u00e0 trung \u0111o\u1ea1n c\u1ea1nh b\u00ean (chi\u1ec1u cao c\u1ee7a h\u00ecnh thang c\u00e2n); $S_1$; $S_2$ di\u1ec7n t\u00edch hai \u0111\u00e1y)<br\/>Khi \u0111\u00f3 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t l\u00e0 $\\left(\\dfrac{4a}{2}+\\dfrac{4.3a}{2}\\right).2a+a^2+(3a^2)=26a^2$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":2}]}],"id_ques":1881},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $48a^2\\sqrt{3}$","B. $48a\\sqrt{3}$","C. $42a^2\\sqrt{3}$"],"ques":"<span class='basic_left'>Cho h\u00ecnh ch\u00f3p c\u1ee5t t\u1ee9 gi\u00e1c \u0111\u1ec1u $ABCD.A\u2019B\u2019C\u2019D\u2019$ c\u00f3 c\u1ea1nh b\u00ean l\u00e0 $8a$; c\u1ea1nh \u0111\u00e1y l\u1edbn b\u1eb1ng $5a$ v\u00e0 \u0111\u00e1y nh\u1ecf b\u1eb1ng $a$. T\u00ednh di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t \u0111\u00f3.<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.15.png' \/><\/center><br\/><b> \u0110\u00e1p s\u1ed1: <\/b> ?(\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)<\/span>","hint":"K\u1ebb trung \u0111o\u1ea1n $A'H$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.15a.png' \/><\/center>X\u00e9t m\u1eb7t b\u00ean $AA'B'B$, k\u1ebb $A'H\\bot AB$.<br\/>Ta c\u00f3 $AH=\\dfrac{AB-A'B'}{2}=\\dfrac{5a-a}{2}=2a$<br\/>X\u00e9t tam gi\u00e1c $A'AH$ vu\u00f4ng t\u1ea1i $H$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$AA'^2=AH^2+A'H^2\\\\ \\Rightarrow A'H^2=16a^2-4a^2\\\\ \\Leftrightarrow A'H=2a\\sqrt{3}$<br\/>V\u1eady di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t l\u00e0 $4.2a\\sqrt{3}.(a+5a)=48a^2\\sqrt{3}$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch)<\/span>"}]}],"id_ques":1882},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/10.jpg' \/><\/center>C\u00f4ng th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u1ec1u v\u00e0 h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng \u0111\u1ec1u c\u00f3 c\u00f9ng chi\u1ec1u cao v\u00e0 di\u1ec7n t\u00edch \u0111\u00e1y.<br\/>(G\u1ecdi th\u1ec3 t\u00edch l\u0103ng tr\u1ee5 l\u00e0 $V_{lt}$ v\u00e0 th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p \u0111\u1ec1u l\u00e0 $V_{c\u0111}$)","select":["A. $V_{lt}=\\dfrac{1}{3}V_{c\u0111}$","B. $V_{lt}=\\dfrac{1}{2}V_{c\u0111}$","C. $V_{c\u0111}=\\dfrac{1}{3}V_{lt}$","D. $V_{c\u0111}=\\dfrac{1}{2}V_{lt}$"],"hint":"","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.14.png' \/><\/center>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p \u0111\u1ec1u b\u1eb1ng $\\dfrac{1}{3}$ di\u1ec7n t\u00edch \u0111\u00e1y nh\u00e2n chi\u1ec1u cao.<br\/>Th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng b\u1eb1ng di\u1ec7n t\u00edch \u0111\u00e1y nh\u00e2n chi\u1ec1u cao.<br\/>Do v\u1eady, th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p \u0111\u1ec1u = $\\dfrac{1}{3}$ th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng c\u00f3 c\u00f9ng chi\u1ec1u cao v\u00e0 di\u1ec7n t\u00edch \u0111\u00e1y. <br\/>Hay:<br\/>$V_{c\u0111}=\\dfrac{1}{3}V_{lt}$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><br\/><span class='basic_green'>Ghi nh\u1edb: <\/span>H\u00ecnh ch\u00f3p \u0111\u1ec1u c\u00f3 di\u1ec7n t\u00edch \u0111\u00e1y l\u00e0 $S$ (\u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch), \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng cao l\u00e0 $h$ (\u0111\u01a1n v\u1ecb \u0111\u1ed9 d\u00e0i).<br\/> Th\u00ec th\u1ec3 t\u00edch l\u00e0 $S=\\dfrac{1}{3}S.h$ (\u0111\u01a1n v\u1ecb th\u1ec3 t\u00edch)<\/span><\/span> ","column":2}]}],"id_ques":1883},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2383,28"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u1ed9 d\u00e0i \u0111\u00e1y b\u1eb1ng $12,4\\,cm$ v\u00e0 \u0111\u01b0\u1eddng cao b\u1eb1ng $15,5 cm$.<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.11.png' \/><\/center><br\/><b> \u0110\u00e1p s\u1ed1: <\/b> _input_ ($cm^3$)<br\/>(<i> K\u1ebft qu\u1ea3 \u0111\u1ec3 d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n <\/i>)","hint":"\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p","explain":"<span class='basic_left'>V\u00ec h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u n\u00ean \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng.<br\/>Di\u1ec7n t\u00edch \u0111\u00e1y l\u00e0 $S=12,4.12,4=153,76\\,(cm^2)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u l\u00e0 $V=153,76.15,5=2383,28\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $2383,28$<\/span><\/span>"}]}],"id_ques":1884},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["40000"],["3"]]],"list":[{"point":5,"width":50,"type_input":"","input_hint":"frac","ques":"T\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u1ed9 d\u00e0i trung \u0111o\u1ea1n $30 cm$ v\u00e0 chi\u1ec1u cao l\u00e0 $20 cm$ nh\u01b0 h\u00ecnh v\u1ebd d\u01b0\u1edbi \u0111\u00e2y.<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.6.png' \/><\/center><br\/><b> \u0110\u00e1p s\u1ed1: <\/b> <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>($cm^3$)<br\/>","hint":"T\u00ednh $OH$","explain":"<span class='basic_left'><br\/>- V\u00ec $S.ABCD$ l\u00e0 ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u n\u00ean $ABCD$ l\u00e0 h\u00ecnh vu\u00f4ng v\u00e0 c\u00e1c m\u1eb7t b\u00ean l\u00e0 c\u00e1c tam gi\u00e1c c\u00e2n.<br\/>+) $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$<br\/>+) $O$ giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng ch\u00e9o.<br\/>- V\u00ec $SO$ l\u00e0 \u0111\u01b0\u1eddng cao n\u00ean $SO \\bot mp(ABCD) \\,\\Rightarrow SO\\bot HO$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.6.png' \/><\/center><br\/>X\u00e9t tam gi\u00e1c $SHO$ vu\u00f4ng t\u1ea1i $O$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$SO^2+OH^2=SH^2\\\\ \\Rightarrow OH^2=30^2-20^2\\\\ \\Leftrightarrow OH^2=500\\\\ \\Leftrightarrow OH=10\\sqrt{5}\\,(cm)$<br\/> Ta c\u00f3, $HA=HB;\\,OA=OC$, suy ra $HO$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c $ABC$.<br\/>Do \u0111\u00f3 $BC=2HO=20\\sqrt{5}\\,(cm)$<br\/>V\u1eady di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng $ABCD$ l\u00e0 $(20\\sqrt{5})^2=2000\\,(cm^2)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p $S.ABCD$ l\u00e0 $\\dfrac{1}{3}.20.2000=\\dfrac{40000}{3}\\,(cm^3)$<\/span>"}]}],"id_ques":1885},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["253,99"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u1ed9 d\u00e0i c\u1ea1nh b\u00ean l\u00e0 $10 cm$ v\u00e0 trung \u0111o\u1ea1n d\u00e0i $8 cm$ nh\u01b0 h\u00ecnh v\u1ebd:<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.8.png' \/><\/center><br\/><b> \u0110\u00e1p s\u1ed1: <\/b> _input_ ($cm^3$)<br\/>(<i> K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai <\/i>)","hint":"T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y.","explain":"<span class='basic_left'><br\/>- V\u00ec $S.ABCD$ l\u00e0 ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u n\u00ean $ABCD$ l\u00e0 h\u00ecnh vu\u00f4ng v\u00e0 c\u00e1c m\u1eb7t b\u00ean l\u00e0 c\u00e1c tam gi\u00e1c c\u00e2n.<br\/>+) $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$<br\/>+) $O$ giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng ch\u00e9o.<br\/>- V\u00ec $SO$ l\u00e0 \u0111\u01b0\u1eddng cao n\u00ean $SO \\bot mp(ABCD) \\,\\Rightarrow SO\\bot HO$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.8.png' \/><\/center>X\u00e9t tam gi\u00e1c $SAH$ vu\u00f4ng t\u1ea1i $H$ c\u00f3 $SH=8\\,cm$ v\u00e0 $SA=10\\,cm$<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$SA^2=SH^2+AH^2\\\\ \\Rightarrow AH^2=10^2-8^2\\\\ \\Leftrightarrow AH^2=36\\\\ \\Leftrightarrow AH=6\\,(cm)$<br\/>Ta c\u00f3 $AH=HB \\Rightarrow AB=2AH=12\\,cm$<br\/>V\u1eady di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng $ABCD$ l\u00e0 $12^2=144\\,(cm^2)$<br\/>Ta c\u00f3, $HA=HB;\\,OA=OC$, suy ra $HO$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c $ABC$.<br\/>Suy ra $HO=6\\,cm$<br\/>X\u00e9t tam gi\u00e1c $SHO$ vu\u00f4ng t\u1ea1i $O$. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$SO^2+OH^2=SH^2\\\\ \\Rightarrow SO^2=8^2-6^2\\\\ \\Leftrightarrow SO^2=28\\\\ \\Leftrightarrow SO=2\\sqrt{7}\\,(cm)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p $S.ABCD$ l\u00e0 $\\dfrac{1}{3}.144.2\\sqrt{7}=253,99\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $253,99$<\/span><\/span>"}]}],"id_ques":1886},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $108\\sqrt{3}$","B. $100\\sqrt{3}$","C. $104\\sqrt{3}$"],"ques":"Cho h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u01b0\u1eddng cao b\u1eb1ng $12 cm$, \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y b\u1eb1ng $6\\sqrt 3 cm$. T\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p.<br\/><b> \u0110\u00e1p s\u1ed1: <\/b> ?($cm^3$)","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago","explain":"<span class='basic_left'><br\/><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> T\u00ednh $CH$<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u00ednh di\u1ec7n t\u00edch $ABC$<br\/><b>B\u01b0\u1edbc 3:<\/b> T\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.17a.png' \/><\/center><br\/>- V\u00ec $S.ABC$ l\u00e0 ch\u00f3p tam gi\u00e1c \u0111\u1ec1u n\u00ean $ABC$ l\u00e0 tam gi\u00e1c \u0111\u1ec1u v\u00e0 c\u00e1c m\u1eb7t b\u00ean l\u00e0 c\u00e1c tam gi\u00e1c c\u00e2n.<br\/>+) $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$<br\/>+) $O$ l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua c\u00e1c \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c $ABC$ (giao \u0111i\u1ec3m ba \u0111\u01b0\u1eddng trung tr\u1ef1c)<br\/>- V\u00ec $SO$ l\u00e0 \u0111\u01b0\u1eddng cao n\u00ean $SO \\bot mp(ABC) \\,\\Rightarrow SO\\bot HO$<br\/>X\u00e9t tam gi\u00e1c $ABC$ \u0111\u1ec1u $CH\\bot AB\\Rightarrow HA=HB=3\\sqrt{3}\\,(cm)$<br\/>X\u00e9t tam gi\u00e1c $ACH$ vu\u00f4ng t\u1ea1i $A$ c\u00f3 $AH=3\\sqrt{3}\\,cm$ v\u00e0 $AC=6\\sqrt{3}\\,cm$<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$AC^2=AH^2+CH^2\\\\ \\Rightarrow CH^2=AC^2-AH^2\\\\ \\Leftrightarrow CH^2=(6\\sqrt{3})^2-(3\\sqrt{3})^2\\\\ \\Leftrightarrow CH^2=81\\\\ \\Leftrightarrow CH=9\\,(cm)$<br\/>Di\u1ec7n t\u00edch $ABC$ l\u00e0 $\\dfrac{1}{2}.6\\sqrt{3}.9=27\\sqrt{3}\\,(cm^2)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p l\u00e0 $\\dfrac{1}{3}.27\\sqrt{3}.12=108\\sqrt{3}\\,(cm^3)$<\/span>"}]}],"id_ques":1887},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1344"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u, c\u00f3 c\u1ea1nh \u0111\u00e1y l\u00e0 $16 cm$ v\u00e0 chi\u1ec1u cao b\u1eb1ng $18 cm$. C\u1eaft h\u00ecnh ch\u00f3p \u0111\u1ec1u b\u1edfi m\u1eb7t ph\u1eb3ng \u0111i qua c\u00e1c trung \u0111i\u1ec3m c\u1ea1nh b\u00ean. T\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p c\u1ee5t \u0111\u01b0\u1ee3c h\u00ecnh th\u00e0nh.<br\/><b> \u0110\u00e1p s\u1ed1: <\/b> _input_ ($cm^3$)","hint":"Th\u1ec3 t\u00edch ch\u00f3p c\u1ee5t b\u1eb1ng th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p l\u1edbn tr\u1eeb \u0111i th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p nh\u1ecf","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.7.png' \/><\/center>X\u00e9t h\u00ecnh ch\u00f3p t\u1eeb gi\u00e1c \u0111\u1ec1u $S.ABCD$ c\u00f3 $SO$ l\u00e0 \u0111\u01b0\u1eddng cao.<br\/>Gi\u1ea3 s\u1eed m\u1eb7t ph\u1eb3ng c\u1eaft c\u00e1c c\u1ea1nh b\u00ean $SA;SB;SC;SD$ v\u00e0 $SO$ l\u1ea7n l\u01b0\u1ee3t t\u1ea1i $A';B';C';D'$ v\u00e0 $O'$<br\/>V\u00ec m\u1eb7t ph\u1eb3ng \u0111i qua c\u00e1c trung \u0111i\u1ec3m c\u1ea1nh b\u00ean n\u00ean $A';B';C'$ v\u00e0 $D'$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh $SA;SB;SC$ v\u00e0 $SD$<br\/>Khi \u0111\u00f3 ta c\u00f3: $A'B'; B'C';C'D'$ v\u00e0 $D'A'$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a c\u00e1c tam gi\u00e1c $SAB$, $SBC$, $SCD$ v\u00e0 $SDA$.<br\/>Suy ra $A'B'=B'C'=C'D'=D'A'=\\dfrac{AB}{2}=8\\,cm$<br\/>V\u00ec v\u1eady \u0111\u00e1y nh\u1ecf l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh $8\\,cm$.<br\/>Ta c\u0169ng c\u00f3 $O'$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $SO$.<br\/>Do \u0111\u00f3, $SO'=\\dfrac{1}{2}SO=9\\,cm$<br\/>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p $S.ABCD$ l\u00e0 $\\dfrac{1}{3}.SO.S_{ABCD}=\\dfrac{1}{3}.18.16^2=1536\\,(cm^3)$<br\/>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p $S.A'B'C'D'$ l\u00e0 $\\dfrac{1}{3}.SO'.S_{A'B'C'D'}=\\dfrac{1}{3}.9.8^2=192\\,(cm^3)$<br\/>V\u1eady th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p c\u1ee5t l\u00e0 $1536-192=1344\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 ph\u1ea3i \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $1344$<\/span><\/span>"}]}],"id_ques":1888},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/8.jpg' \/><\/center>Cho h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u $S.ABC$; $H$ l\u00e0 trung \u0111i\u1ec3m $AB$ v\u00e0 $SO$ l\u00e0 \u0111\u01b0\u1eddng cao. T\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p bi\u1ebft h\u00ecnh ch\u00f3p c\u00f3 t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh \u0111\u1ec1u b\u1eb1ng $2 cm$..","select":["A. $\\dfrac{\\sqrt{24}}{\\sqrt 3}\\,cm^3$","B. $\\dfrac{\\sqrt{8}}{\\sqrt 3}\\,cm^3$","C. $\\dfrac{\\sqrt{2}}{3}\\,cm^3$","D. $\\dfrac{\\sqrt{8}}{3}\\,cm^3$"],"hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago \u0111\u1ec3 t\u00ednh $CH$ v\u00e0 $SO$","explain":" <span class='basic_left'>- V\u00ec $S.ABC$ l\u00e0 ch\u00f3p tam gi\u00e1c \u0111\u1ec1u n\u00ean $ABC$ l\u00e0 tam gi\u00e1c \u0111\u1ec1u v\u00e0 c\u00e1c m\u1eb7t b\u00ean l\u00e0 c\u00e1c tam gi\u00e1c c\u00e2n.<br\/>+) $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$<br\/>+) $O$ t\u00e2m c\u1ee7a tam gi\u00e1c $ABC$ (giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng trung tr\u1ef1c)<br\/>- V\u00ec $SO$ l\u00e0 \u0111\u01b0\u1eddng cao n\u00ean $SO \\bot mp(ABC) \\,\\Rightarrow SO\\bot CH$<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/hinhhoc/bai22/lv1/img\/H8_B22_D1.19.png' \/><\/center>X\u00e9t tam gi\u00e1c $AHC$ vu\u00f4ng t\u1ea1i $H$ c\u00f3: $AC=2\\,cm$ v\u00e0 $AH=1\\,cm$<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3:<br\/>$HC=\\sqrt{AC^2-AH^2}\\\\ \\Rightarrow HC=\\sqrt{4-1}\\\\ \\Leftrightarrow HC=\\sqrt{3}\\,(cm)$<br\/>Di\u1ec7n t\u00edch tam gi\u00e1c $ABC$ l\u00e0 $\\dfrac{1}{2}CH.AB=\\sqrt 3\\,(cm^2)$<br\/>V\u00ec $O$ l\u00e0 t\u00e2m c\u1ee7a tam gi\u00e1c \u0111\u1ec1u n\u00ean $O$ \u0111\u1ed3ng th\u1eddi l\u00e0 giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng trung tuy\u1ebfn.<br\/>Theo t\u00ednh ch\u1ea5t v\u1ec1 tr\u1ecdng t\u00e2m tam gi\u00e1c, ta c\u00f3 $CO=\\dfrac{2}{3}CH=\\dfrac{2\\sqrt 3}{3}\\,(cm)$<br\/>X\u00e9t tam gi\u00e1c $SOC$ vu\u00f4ng t\u1ea1i $O$ c\u00f3: $SC=2 cm$ v\u00e0 $CH=\\dfrac{2\\sqrt 3}{3}\\,cm$<br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago ta c\u00f3: <br\/>$SO=\\sqrt{SC^2-CO^2}\\\\ \\Rightarrow SO=\\sqrt{4-\\dfrac{4}{3}}=\\sqrt{\\dfrac{8}{3}}\\,(cm)$<br\/>V\u1eady th\u1ec3 t\u00edch $S.ACB$ l\u00e0 $\\dfrac{1}{3}.\\sqrt{3}\\sqrt{\\dfrac{8}{3}}=\\dfrac{\\sqrt{8}}{3}\\,(cm^3)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span>","column":2}]}],"id_ques":1889}],"lesson":{"save":0,"level":1}}