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Surface Area Formula for Prisms

Surface Area Formula for Prisms
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2023-12-28 21:36
Solid GeometryGeometric ConstructionSlider AnimationGraphing
This example demonstrates how to calculate the surface area of a prism using its net. Core math concepts include lateral area and surface area formulas for prisms. Construction highlights the use of GeoGebra commands like Polygon, Net, and Prism. Suitable for grades 6-8, focusing on applying formulas to find prism surface areas.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

The figure includes a triangular prism and a square prism, each with an unfolded net. Labels for height and side lengths are shown. The triangular prism has a triangular base, and the square prism has a square base. Both prisms are displayed in a 3D view with their surface nets and annotations. The figure illustrates the method of calculating surface area of prisms.
The prompt above was compiled from the original drawing commands and is for reference only.