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Volume of Square Pyramid

Volume of Square Pyramid
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2017-05-05 08:50
Solid GeometryGeometric Construction
This example demonstrates the calculation of the volume of a square pyramid, illustrating the formula and its application. Key math concepts include solid geometry volume formulas, the relationship between cubes and pyramids, and similarity transformations. Construction highlights involve using commands like Point, Segment, Polygon, Prism, Net, Pyramid, and objects such as a, A, B, f, poly1, g, h, i, j, C, D, b, E, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH to construct the pyramid and its net, showcasing geometric relationships. Suitable for high school solid geometry instruction and volume calculation practice.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → f
  3. Polygon(A, B, 4) → poly1, g, h, i, j, C, D
  4. Prism(poly1, a) → b, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  5. Net(b, c) → d, I, R, S, T, U, V, faceIJKL, faceIJNM, faceJKPO, faceKLRQ, faceILST, J, faceMNUV, edgeIJ, edgeJK, edgeKL, edgeIL, edgeIM, edgeMN, edgeJN, edgeJO, edgeOP, K, edgeKP, edgeKQ, edgeQR, edgeLR, edgeLS, edgeST, edgeIT, edgeNU, edgeUV, edgeMV, L, M, N, O, P, Q
  6. Pyramid(faceMNUV, (-(a / 2))) → e, W, faceMNW, faceNUW, faceUVW, faceMVW, edgeMW, edgeNW, edgeUW, edgeVW
  7. Pyramid(faceIJNM, (-(a / 2))) → k, Z, faceIJZ, faceJNZ, faceMNZ, faceIMZ, edgeIZ, edgeJZ, edgeNZ, edgeMZ
  8. Pyramid(faceIJKL, a / 2) → l, A_1, face1, face3, face4, face2, edge1, edge2, edge3, edge4
  9. Pyramid(faceJKPO, (-(a / 2))) → m, B_1, face5, face7, face8, face6, edge5, edge6, edge8, edge7
  10. Pyramid(faceILST, (-(a / 2))) → n, C_1, face9, face10, face12, face11, edge10, edge9, edge12, edge11
  11. Pyramid(faceKLRQ, (-(a / 2))) → o, D_1, face13, face15, face16, face14, edge13, edge14, edge16, edge15
  12. Point(Circle[E_1, a]) → F_1
  13. Segment(E_1, F_1) → p
  14. Polygon(E_1, F_1, 4) → poly2, q, r, s, t, G_1, H_1
  15. Prism(poly2, a) → u, I_1, edge17, edge18, edge19, edge20, edge21, edge23, edge24, edge22, J_1, K_1, L_1, face17, face19, face20, face18, face21

AI Drawing Prompt Reference

Draw a square pyramid with its base square, four triangular sides, and the net of the pyramid. Start by drawing the base square, then construct the four triangular sides, and finally draw the pyramid's net to show the geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.