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Volume of a Pyramid by Miguel Quinonez

Volume of a Pyramid by Miguel Quinonez
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2017-10-04 03:23
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to construct and calculate the volume of a pyramid using GeoGebra. Key math concepts include volume formulas, 3D coordinates, polygon construction, and analytical geometry. The construction utilizes commands like Polygon, Point, Pyramid, Net, Intersect, and Segment. Suitable for high school solid geometry education or for math enthusiasts exploring geometric volume calculations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 8) → poly1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  2. Point(zAxis) → I
  3. Pyramid(poly1, I) → a, faceABI, edgeBI, edgeCI, edgeDI, edgeEI, edgeFI, edgeGI, edgeHI, faceBCI, faceCDI, faceDEI, faceEFI, faceFGI, faceGHI, faceAHI, edgeAI
  4. Net(a, b) → c, J, S, T, U, V, W, Z, A_1, faceJKLMNOPQ, faceJKR, faceKLS, K, faceLMT, faceMNU, faceNOV, faceOPW, facePQZ, face1, edgeJK, edgeKL, edgeLM, edgeMN, L, edgeNO, edgeOP, edgePQ, edgeJQ, edgeJR, edgeKR, edgeKS, edgeLS, edgeLT, edgeMT, M, edgeMU, edgeNU, edgeNV, edgeOV, edgeOW, edgePW, edgePZ, edgeQZ, edge2, edge1, N, O, P, Q, R
  5. Intersect(xAxis, yAxis) → B_1
  6. Intersect(edgeOV, edgePZ) → C_1
  7. Segment(B_1, C_1) → n
  8. Intersect(yAxis, edgeNO) → D_1
  9. Segment(D_1, C_1) → q
  10. Segment(D_1, B_1) → r
  11. Segment(B_1, C_1) → s
  12. Segment(D_1, B_1) → p
  13. Intersect(edgeFI, edgeGI) → E_1
  14. Segment(B_1, E_1) → t
  15. Point(edgeNO) → F_1
  16. Point(edgeNO) → G_1
  17. Polygon(F_1, G_1, B_1) → t1, b_1, f_1, g_1
  18. Segment(E_1, B_1) → e
  19. Intersect(edgeNV, edgeOV) → H_1
  20. Segment(D_1, H_1) → h_1
  21. Segment(E_1, D_1) → i_1