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Volume of a Square-Based Pyramid

Volume of a Square-Based Pyramid
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2019-08-09 23:33
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the volume calculation of a square-based pyramid. Key mathematical concepts include the volume formula for a pyramid and geometric construction. Using GeoGebra commands such as Cube, Net, Polygon, and Pyramid, the various faces and edges of the pyramid can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Cube(A, B, C) → Cube, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  2. Net(Cube, b) → c, I, R, S, T, U, V, faceIJKL, faceILNM, faceIJRQ, faceJKTS, faceKLVU, J, faceMNOP, edgeIL, edgeIJ, edgeJK, edgeKL, edgeLN, edgeMN, edgeIM, edgeIQ, edgeQR, K, edgeJR, edgeJS, edgeST, edgeKT, edgeKU, edgeUV, edgeLV, edgeNO, edgeOP, edgeMP, L, M, N, O, P, Q
  3. Polygon(M, N, O, P) → q1, m, n, o, p
  4. Pyramid(q1, a / 2) → d, W, faceMNW, faceNOW, faceOPW, faceMPW, edgeMW, edgeNW, edgeOW, edgePW
  5. Polygon(I, L, N, M) → q2, i, l, n_1, m_1
  6. Pyramid(q2, a / 2) → e, Z, faceILZ, faceLNZ, faceMNZ, faceIMZ, edgeIZ, edgeLZ, edgeNZ, edgeMZ
  7. Polygon(K, L, V, U) → q3, k, l_1, v, u
  8. Pyramid(q3, ((-a)) / 2) → f, A_1, face1, face3, face4, face2, edge1, edge2, edge4, edge3
  9. Polygon(K, J, S, T) → q4, k_1, j, s, t
  10. Polygon(I, Q, R, J) → q5, i_1, q, r, j_1
  11. Pyramid(q5, a / 2) → g, B_1, face6, face8, face7, face5, edge5, edge7, edge8, edge6
  12. Pyramid(q4, a / 2) → h, C_1, face9, face10, face12, face11, edge10, edge9, edge11, edge12
  13. Polygon(J, I, L, K) → q6, j_2, i_2, l_2, k_2
  14. Pyramid(q6, ((-a)) / 2) → w, D_1, face13, face14, face16, face15, edge14, edge13, edge16, edge15