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棱柱表面积公式

棱柱表面积公式
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2023-12-28 21:36
立体几何几何作图滑块动画函数图像
本范例通过棱柱的展开图演示如何计算棱柱的表面积。涉及的核心数学概念包括棱柱的侧面积和表面积公式。作图要点使用了GeoGebra命令如Polygon（多边形）、Net（展开图）、Prism（棱柱）等。适合6-8年级学生，用于学习如何应用公式计算棱柱的表面积。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.6146013788884067, 0.3910301478907354, 0.25063041309811407, 0.18401369615601934, 0.14888606996758716, 0.24522672871004, 0.5249032995797539, 0.4630769647957783, 0.7536624286138123, 0.25664999940461236, 0.01027474017769167, 0.8259921454253121, 0.7729610962147958, 0.6267768372382769, 0.8736916869563132, 0.5694939567057786, 0.37282520877791475, 0.40987966323650216, 0.8849313190238259, 0.8704320867230569, 0.9087295307096195, 0.31561192486769035, 0.8627303084833257, 0.8905016898321548, 0.4081840016614268, 0.9483058368098913, 0.238769669545516, 0.0468504417230774, 0.9739891915573577, 0.4831344333827042, 0.6253491476780035, 0.5646663474429795, 0.4164523128784363, 0.8926791963941189, 0.4733947360205672, 0.02795827403006978, 0.6591525265041692, 0.3517698811173417, 0.6466914920420561, 0.3607860123878545, 0.7425602294516331, 0.16372800485903607, 0.5359194655252721, 0.8831788866012328, 0.07297001617424703, 0.35734527295014223, 0.6421927231161242, 0.6539023049325892, 0.13079846330615055, 0.9610681887401481, 0.7843635283526064, 0.34608851824348347, 0.7423272760793201, 0.5389352115745214, 0.14735000021585845, 0.05154334287533762, 0.6324388712351955, 0.7518271761284174, 0.9501826810391677, 0.04527228198600113, 0.6227963657769308, 0.34754270098371065, 0.48233753946791086, 0.9234404251774914, 0.23026103954858657, 0.01409861356114997, 0.8852336303607192, 0.3255868411482091, 0.2941202240098167, 0.3724821973791268, 0.08252222295644075, 0.6154600326624263, 0.3779147760898981, 0.6078453050606676, 0.16797890629263842, 0.1843226208005086, 0.14231040627948383, 0.791831669782986, 0.1834339814357897, 0.835994114973157, 0.45954797244005724, 0.5933674398646661, 0.8112366096712069, 0.2842574561219884, 0.25753778866985116, 0.5108212034357905, 0.4762461058561912, 0.630550190957327, 0.9226298191385126, 0.4749532380887925, 0.7312797712103626, 0.32309377462531835, 0.1744954628604052, 0.20952512216567287, 0.23731952547405163, 0.977783766977875, 0.45439878510730014, 0.454829353780107, 0.5355895606434894, 0.10627188497585707, 0.7794142901368996, 0.8887248751433058, 0.882866480708439, 0.7777152567884618, 0.5398651744594025, 0.21002806871299293, 0.8940676506026274, 0.057650975178169556, 0.0654100074156694, 0.6403099223719819, 0.20728762113924037, 0.8803735165400353, 0.296798018552243, 0.08228869752300097, 0.6760120551415018, 0.12005071002820364, 0.40534210967912954, 0.5360837979419001, 0.49123765438955747, 0.3806081711815409, 0.37062574028789713, 0.8386100236240234, 0.34266110579624376, 0.20514491996319714, 0.7088639402919856, 0.08634244525283678, 0.44297398197191595, 0.34231291220583104, 0.26968068044422755, 0.397571370906155, 0.48261046780011285, 0.649700072053545, 0.5378438816723606, 0.5870921138753665, 0.5840431896782382, 0.6628021864142476, 0.4987166796280578, 0.024039138035708014, 0.47490776345712066, 0.3926505537221595, 0.9318369523940958, 0.27227397863947983, 0.45785989497783086, 0.7855830057103675, 0.3061299162757121, 0.0723762749614693, 0.5321293291110499, 0.7350027592084476, 0.8027870793742421, 0.08486261572319151, 0.9372328263794103, 0.3672645705111558, 0.9178122459245601, 0.2557716538419389, 0.7232442554246804, 0.022060577320195195, 0.875639122563682, 0.5182056659797107, 0.40439270360608903, 0.21184742940993773, 0.6180669987704255, 0.8568066148436159, 0.7235698759780479, 0.47496407133646584, 0.669040706888731, 0.9164716358738938, 0.5545766238896299, 0.07313475703831589, 0.9555167979057159, 0.5518759857005878, 0.3266235514814822, 0.13603367669003516, 0.9878136100844618, 0.000573276907673368, 0.20172364862615788, 0.07350780468480726, 0.03943324461200676, 0.6295806120750228, 0.010175866125899434, 0.5599123490109739, 0.8863740161840487, 0.5934335602898578, 0.2623363030757144, 0.8548073901380723, 0.6194178634522189, 0.8807084984547978, 0.10630911710029527, 0.7399973021849494, 0.0897817447325394, 0.9759615328324251, 0.7710626759717689, 0.7945642262960643, 0.49886436744229323, 0.40492216458562375, 0.3427865752265809, 0.4771541894441164, 0.28659778761757493, 0.10260515196552675, 0.7290537358340974, 0.7483197853592514}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. If(countQuestion ≟ 0, 4, floor((currentRandomSeeds(2) * 5)) + 1) → randomSideLength
  4. KeepIf(Mod[randomSideLength, kk] ≟ 0, kk, Sequence[randomSideLength]) → l1
  5. If(countQuestion ≟ 0, 1, Element[l1, floor((currentRandomSeeds(4) * Length[l1])) + 1]) → heiFact
  6. If(countQuestion ≟ 0, 2, (floor((currentRandomSeeds(1) * 4)) + 1) / heiFact) → hei_{1}
  7. If(currentRandomSeeds(3) ≤ 0.5 ∨ countQuestion ≟ 0, 4, 3) → Case
  8. If(Case ≟ 4, hei_{1} + 3, (hei_{1} * sin(30°)) + 1.5) → ymax
  9. Polygon((0, 0), (1, 0), 3) → poly1
  10. Centroid(poly1) → B
  11. Translate(poly1, Vector[B, (0, 1)]) → baseTri
  12. Prism(baseTri, hei_{1}) → prism3, G, edge10, edgeGH, edgeHI, edgeGI, H, I, face5, face7, face6, faceGHI, edge7, edge9
  13. Net(prism3, tCil2) → c, J, S, faceJKL, faceJKNM, faceKLPO, faceJLQR, faceMNS, edge26, edge30, edge27, edge28, K, edge35, edge31, edge32, edge38, edge33, edge34, edge39, edge29, edge37, edge36, L, M, N, O, P, Q, R
  14. Midpoint(edge26) → LabelTriPos
  15. Segment(L, LabelTriPos) → triHeight
  16. Textfield(input1) → InputBox1
  17. Segment((0, 1, 0), (1, 1, 0)) → segRad_{1}
  18. Rotate((0, 0, hei_{1}), (pi / 2 * tCil_{1}), Line[(1, 0, 0), (-1, 0, 0)]) → TopPoint
  19. Vector((0, cos((tCil_{1} * pi)), (-sin((tCil_{1} * pi))))) → u
  20. Vector((0, sin((tCil_{1} * pi)), cos((tCil_{1} * pi)))) → v
  21. Corner(5) → App2DSize
  22. Translate(f, Vector[(Vector[Corner[4], Corner[1]] / 500 * 16)]) → f'
  23. Polygon({(-0.5, 1, 0), (0.5, 1, 0), (0.5, 0, 0), (-0.5, 0, 0)}) → baseSqare
  24. Prism(baseSqare, (-hei_{1})) → prism4, C, edge1, edge2, edge3, edge4, edgeCD, edgeDE, edgeEF, edgeCF, D, E, F, face1, face3, face4, face2, faceCDEF
  25. Net(prism4, tCil2) → a, W, N_1, O_1, P_1, Q_1, R_1, face8, face9, face11, face12, face10, Z, face13, edgeWZ, edge11, edge14, edge5, edge6, edge19, edge12, edge13, edge22, A_1, edge15, edge16, edge23, edge17, edge18, edge24, edge8, edge21, edge25, edge20, B_1, C_1, D_1, I_1, K_1, M_1
  26. CornerThreeD(-1, 9) → App3DSize
  27. Midpoint(edge15) → LabelHPos
  28. Midpoint(edge5) → LabelSqPos
  29. Vector((1; (pi / 2 * tCil2) + (pi / 6 * (1 - tCil2)); ((-pi)) / 2 + ((0.8 * pi / 2) * (1 - tCil2)))) → view
  30. CornerThreeD(-1, 13) → A
  31. Midpoint(edge32) → LabelHPos3
  32. Text(hei2, If[Case ≟ 3, LabelHPos3, LabelHPos], true, true) → text5
  33. Distance(Corner[text7, 2], Corner[text7, 1]) → widLabelSide
  34. Text(randomSideLength, LabelTriPos - ((tCil2 * widLabelSide / 2), 0), true, true) → text4
  35. Distance(Corner[text7, 4], Corner[text7, 1]) → heiLabelSide
  36. Translate(L, Vector[(x(O) + 0.1, 0, 0)]) → L'
  37. Translate(LabelTriPos, Vector[(x(O) + 0.1, 0, 0)]) → LabelTriPos'
  38. Segment(L', LabelTriPos') → triHeight'
  39. Text(triHeightNum, Midpoint[triHeight'] + (If[x(O) ≥ 3, -1, 0], heiLabelSide / 2), true, true) → text8
  40. Text(randomSideLength, LabelSqPos + (0, 0.25, (0.25 * tCil2)), true, true) → text6
  41. Vector(Midpoint[triHeight'], Vertex[triHeight', 1]) → w
  42. Vector(Midpoint[triHeight'], Vertex[triHeight', 2]) → b
  43. Zip(("edge" * kk), kk, {5, 15, 26, 32}) → edges

AI 绘图提示语参考

该图形包含一个三角形棱柱和一个正方形棱柱，每个棱柱都展示了其展开图。图中标注了棱柱的高度和边长等参数。三角形棱柱的底面为三角形，正方形棱柱的底面为正方形。两个棱柱在三维视图中呈现，并带有相应的表面展开图和标注信息。图形用于直观展示棱柱的表面面积计算方法。
以上提示语为根据原始绘图命令整理而来，仅供参考。