Hình lăng trụ đứng tam giác và hình lăng trụ đứng tứ giác

Home Toán lớp 7 - tập 2 Chương 10: Một số hình khối trong thực tiễn Bài 37: Hình lăng trụ đứng tam giác và hình lăng trụ đứng tứ giácBài tập nâng cao

{"common":{"save":0,"post_id":"5853","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8024","post_id":"5853","mon_id":"1158532","chapter_id":"1158663","question":"Cho hình l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam giác ABC.A'B'C' có \u0111áy là tam giác vuông. Bi\u1ebft AB = 5 cm, AC = 12 cm và AA' = 14 cm, hãy tính th\u1ec3 tích c\u1ee7a l\u0103ng tr\u1ee5 ABC.A'B'C'.<\/p><svg height=\"200\" width=\"200\"> <g><title><\/title><rect fill=\"#fff\" height=\"202\" id=\"canvas_background\" width=\"202\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_6\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_8\" transform=\"rotate(-152.03839111328125 103.08937072753906,102.3547592163086) \"> <path d=\"m46.35994,78.85475l0,-59l114.00001,59l-114.00001,0z\" fill=\"#ffffff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(152.76795959472656 103.35994720458984,49.35475158691406) \"><\/path> <path d=\"m45.35994,184.85475l0,-58.99999l114.00001,58.99999l-114.00001,0z\" fill=\"#ffffff\" id=\"svg_2\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-width=\"1.5\" transform=\"rotate(152.76795959472656 102.35994720458984,155.35476684570312) \"><\/path> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"40\" x2=\"39.5125\" y1=\"48.05\" y2=\"156\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"168\" x2=\"167.5125\" y1=\"48.05\" y2=\"156\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"140\" x2=\"139.5125\" y1=\"-1.95\" y2=\"106\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(90 103.75624847412108,155.5249938964844) \" x1=\"104\" x2=\"103.5125\" y1=\"92.05\" y2=\"219\"><\/line> <\/g> <rect fill=\"none\" height=\"14\" id=\"svg_9\" stroke=\"#000000\" stroke-width=\"1.5\" width=\"12\" x=\"20.5125\" y=\"164.05\"><\/rect> <rect fill=\"#fff\" height=\"13\" id=\"svg_10\" stroke=\"#000\" stroke-width=\"1.5\" width=\"12\" x=\"71.5125\" y=\"72.05\"><\/rect> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_11\" stroke=\"#000000\" stroke-width=\"0\" text-anchor=\"start\" x=\"3.5125\" xml:space=\"preserve\" y=\"193.05\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_12\" stroke=\"#000000\" stroke-width=\"0\" text-anchor=\"start\" x=\"1.5125\" xml:space=\"preserve\" y=\"123.05\">B<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_13\" stroke=\"#000000\" stroke-width=\"0\" text-anchor=\"start\" x=\"138.5125\" xml:space=\"preserve\" y=\"197.05\">C<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_14\" stroke=\"#000000\" stroke-width=\"0\" text-anchor=\"start\" x=\"67.5125\" xml:space=\"preserve\" y=\"112.05\">A'<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_15\" stroke=\"#000000\" stroke-width=\"0\" text-anchor=\"start\" x=\"45.5125\" xml:space=\"preserve\" y=\"32.05\">B'<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_16\" stroke=\"#000000\" stroke-width=\"0\" text-anchor=\"start\" x=\"178.5125\" xml:space=\"preserve\" y=\"77.05\">C'<\/text> <\/g> <\/svg><\/span><\/p>","options":["A. <\/strong>420 cm²","B. <\/strong>420 cm","C. <\/strong>420 cm³","D. <\/strong>840 cm³"],"correct":"3","level":"3","hint":"Th\u1ec3 tích c\u1ee7a hình l\u0103ng tr\u1ee5 \u0111\u1ee9ng là $V=S_{\u0111\u00e1y}.h$<\/span><\/span>  (v\u1edbi  $S_{\u0111\u00e1y}$<\/span> là di\u1ec7n tích m\u1eb7t \u0111áy, $h$<\/span> là chi\u1ec1u cao)<\/p>(Hình l\u0103ng tr\u1ee5 \u0111\u1ee9ng ABC.A'B'C' có m\u1eb7t \u0111áy là tam giác ABC vuông \u1edf A, chi\u1ec1u cao là AA')<\/p>","answer":"Vì tam giác ABC là tam giác vuông nên di\u1ec7n tích m\u1eb7t \u0111áy là:<\/p>$S_{\u0111\u00e1y}=\\dfrac{1}{2}.AB.AC=\\dfrac{1}{2}.5.12=30\\space$<\/span>(cm²)<\/p>Th\u1ec3 tích hình l\u0103ng tr\u1ee5 ABC.A'B'C' là:<\/p>V = $S_{\u0111\u00e1y}.AA$<\/span> = 30 . 14 = 420 (cm³)<\/p>\u0110áp án \u0111úng là C. <\/strong>420 cm³<\/span><\/p>","type":"choose","extra_type":"shape1","time":"0","user_id":"131","test":"1","date":"2022-05-17 08:18:13","option_type":"txt","len":0},{"id":"8027","post_id":"5853","mon_id":"1158532","chapter_id":"1158663","question":"Tính di\u1ec7n tích xung quanh c\u1ee7a hình l\u0103ng tr\u1ee5 \u0111\u1ee9ng ABCD.A'B'C'D' có các kích th\u01b0\u1edbc nh\u01b0 hình v\u1ebd (các c\u1ea1nh có cùng \u0111\u01a1n v\u1ecb dm).<\/p> <svg height=\"250\" width=\"230\"> <g><title><\/title><rect fill=\"#fff\" height=\"252\" id=\"canvas_background\" width=\"232\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_1\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_16\"> <g id=\"svg_6\"> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"29.0125\" x2=\"211.0125\" y1=\"25.84375\" y2=\"26\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"49.0125\" x2=\"143.0125\" y1=\"82.84375\" y2=\"82.84375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"30.0125\" x2=\"48.0125\" y1=\"25.84375\" y2=\"83.84375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"210.0125\" x2=\"143.0125\" y1=\"26.84375\" y2=\"82.84375\"><\/line> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_7\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"29.0125\" x2=\"211.0125\" y1=\"161.84375\" y2=\"162\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_8\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"49.0125\" x2=\"143.0125\" y1=\"218.84375\" y2=\"218.84375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_9\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"30.0125\" x2=\"48.0125\" y1=\"161.84375\" y2=\"219.84375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"210.0125\" x2=\"143.0125\" y1=\"162.84375\" y2=\"218.84375\"><\/line> <line fill=\"none\" id=\"svg_12\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"30.0125\" x2=\"30\" y1=\"25.84375\" y2=\"163.84375\"><\/line> <line fill=\"none\" id=\"svg_13\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"208.0125\" x2=\"208\" y1=\"25.84375\" y2=\"163.84375\"><\/line> <line fill=\"none\" id=\"svg_14\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"48.0125\" x2=\"48\" y1=\"80.84375\" y2=\"218.84375\"><\/line> <line fill=\"none\" id=\"svg_15\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"144.0125\" x2=\"144\" y1=\"81.84375\" y2=\"219.84375\"><\/line> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"7.0125\" xml:space=\"preserve\" y=\"27.84375\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"50.0125\" xml:space=\"preserve\" y=\"106.84375\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"149.0125\" xml:space=\"preserve\" y=\"98.84375\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_20\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"210.0125\" xml:space=\"preserve\" y=\"22.84375\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_21\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"4.0125\" xml:space=\"preserve\" y=\"179.84375\">A'<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_22\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"31.0125\" xml:space=\"preserve\" y=\"242.84375\">B'<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_23\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"135.0125\" xml:space=\"preserve\" y=\"242.84375\">C'<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_24\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"206.0125\" xml:space=\"preserve\" y=\"188.84375\">D'<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_11\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"25.0125\" xml:space=\"preserve\" y=\"199.84375\">7<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_25\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"88.0125\" xml:space=\"preserve\" y=\"74.84375\">10<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_26\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"180.0125\" xml:space=\"preserve\" y=\"204.84375\">8<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_27\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"89.0125\" xml:space=\"preserve\" y=\"19.84375\">12 dm<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_28\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"8.0125\" xml:space=\"preserve\" y=\"109.84375\">11<\/text> <\/g> <\/svg><\/span><\/p>","options":["A. <\/strong>417 dm²","B. <\/strong>407 dm²","C. <\/strong>407 dm","D. <\/strong>470 dm²"],"correct":"2","level":"3","hint":"","answer":"Chu vi m\u1eb7t \u0111áy là:<\/p>7 + 8 + 10 + 12 = 37 (dm)<\/p>Di\u1ec7n tích xung quanh c\u1ee7a hình l\u0103ng tr\u1ee5 \u0111\u1ee9ng ABCD.A'B'C'D' là:<\/p>37 . 11 = 407 (dm²)<\/p>\u0110áp án \u0111úng là  <\/span>B. <\/strong>407 dm²<\/span><\/p>","type":"choose","extra_type":"shape2","time":"0","user_id":"131","test":"1","date":"2022-05-17 08:40:59","option_type":"txt","len":0},{"id":"8036","post_id":"5853","mon_id":"1158532","chapter_id":"1158663","question":"Tính di\u1ec7n tích xung quanh c\u1ee7a hình l\u0103ng tr\u1ee5 \u0111\u1ee9ng DEF.D'E'F', bi\u1ebft tam giác DEF là tam giác \u0111\u1ec1u c\u1ea1nh a và DD' = a (a > 0).<\/p><svg height=\"200\" width=\"200\"> <g><title><\/title><rect fill=\"#fff\" height=\"202\" id=\"canvas_background\" width=\"202\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_6\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><path d=\"m40.35994,102.85475l0,-59l114.00001,59l-114.00001,0z\" fill=\"#ffffff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(152.76795959472656 97.35994720458986,73.35475158691406) \"><\/path> <path d=\"m39.35994,208.85475l0,-58.99999l114.00001,58.99999l-114.00001,0z\" fill=\"#ffffff\" id=\"svg_2\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-width=\"1.5\" transform=\"rotate(152.76795959472656 96.35994720458983,179.35476684570312) \"><\/path> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"34\" x2=\"33.5125\" y1=\"72.05\" y2=\"180\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"162\" x2=\"161.5125\" y1=\"72.05\" y2=\"180\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"134\" x2=\"133.5125\" y1=\"22.05\" y2=\"130\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(90 97.75624847412108,179.5249938964844) \" x1=\"98\" x2=\"97.5125\" y1=\"116.05\" y2=\"243\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"15.5125\" xml:space=\"preserve\" y=\"69.05\">D<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_9\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"114.5125\" xml:space=\"preserve\" y=\"19.05\">E<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_10\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"173.5125\" xml:space=\"preserve\" y=\"86.05\">F<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_11\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"8.5125\" xml:space=\"preserve\" y=\"188.05\">D'<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_12\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"108.5125\" xml:space=\"preserve\" y=\"127.05\">E'<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_13\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"165.5125\" xml:space=\"preserve\" y=\"186.05\">F'<\/text> <\/g> <\/svg><\/span><\/p>","options":["3a²","3a³","a²","$\\dfrac{1}{2}$<\/span>a²"],"correct":"1","level":"3","hint":"Hình l\u0103ng tr\u1ee5 \u0111\u1ee9ng DEF.D'E'F' có \u0111áy là tam giác \u0111\u1ec1u DEF c\u1ea1nh a và chi\u1ec1u cao DD' = a.<\/p>Di\u1ec7n tích xung quanh c\u1ee7a hình l\u0103ng tr\u1ee5 \u0111\u1ee9ng là $S_{xq}=$<\/span><\/span> C . h<\/span> (v\u1edbi C là chu vi \u0111áy, h là chi\u1ec1u cao)<\/p>","answer":"Chu vi m\u1eb7t \u0111áy là: C = a + a + a = 3a<\/p>Di\u1ec7n tích xung quanh c\u1ee7a hình l\u0103ng tr\u1ee5 \u0111\u1ee9ng là: <\/p>C . h = 3a . a = 3a²<\/p>\u0110áp án \u0111úng là 3a²<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-05-18 08:48:56","option_type":"math","len":0}]}