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Calculating Surface Area of a Regular Pentagon

Calculating Surface Area of a Regular Pentagon
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2017-05-27 00:22
PolygonSolid GeometryGeometric Construction
This example demonstrates the calculation of the surface area of a regular pentagon. It involves core mathematical concepts such as polygon area formulas and surface area calculations in solid geometry for pyramids. The construction uses commands like Polygon, Midpoint, OrthogonalLine, Intersect, Point, Pyramid, Net, and PointIn to create the pentagon, determine key points, find intersections, build the pyramid, and visualize the net. It is suitable for high school students learning about polygons and solid geometry calculations.

GeoGebra Commands & Parameters

  1. Polygon(B, C, 5) → poly1, f, g, h, i, j, D, E, F
  2. Midpoint(i) → G
  3. Midpoint(h) → H
  4. OrthogonalLine(G, i) → k
  5. OrthogonalLine(H, h) → l
  6. Intersect(k, l) → I
  7. Point(zAxis) → A
  8. Pyramid(poly1, A) → a, faceABC, edgeAF, faceACD, faceADE, faceAEF, faceABF, edgeAB, edgeAC, edgeAD, edgeAE
  9. Net(a, b) → c, J, S, faceJKLMN, faceJKO, faceKLP, faceLMQ, faceMNR, faceJNS, edgeJK, edgeKL, edgeLM, K, edgeMN, edgeJN, edgeJO, edgeKO, edgeKP, edgeLP, edgeLQ, edgeMQ, edgeMR, edgeNR, L, edgeNS, edgeJS, M, N, O, P, Q, R
  10. PointIn(faceJKLMN) → PointfaceJKLMN
  11. PointIn(faceLMQ) → PointfaceLMQ
  12. PointIn(faceMNR) → PointfaceMNR
  13. PointIn(faceJNS) → PointfaceJNS
  14. PointIn(faceJKO) → PointfaceJKO
  15. PointIn(faceKLP) → PointfaceKLP