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Area of Square Pyramid

Area of Square Pyramid
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2012-04-05 12:00
PolygonSolid GeometryGeometric Construction
In collections Area and Volume (III) S.3 Ch.5 Area and Volume (III)-1 S.3 Ch.5 Area and Volume (III)-2
This example demonstrates a square base and four congruent isosceles triangles forming a pyramid. Key mathematical concepts include square, isosceles triangle, and solid geometry. Using GeoGebra commands such as Circle, Point, Intersect, Polygon, Midpoint, Line, Angle, Rotate, the geometric figure is constructed. Suitable for students at middle school level and above.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Point(c) → B
  3. Circle(B, a) → d
  4. Intersect(c, d) → C, D, ,
  5. Point(d) → E
  6. Circle(E, a) → e
  7. Intersect(e, c) → F, G, ,
  8. Polygon(A, B, E, G) → poly1, a_1, b, e_1, g
  9. Midpoint(g) → H
  10. Midpoint(e_1) → I
  11. Midpoint(b) → J
  12. Midpoint(a_1) → K
  13. Line(K, I) → f
  14. Line(H, J) → h_1
  15. Intersect(h_1, f) → L
  16. Circle(L, a + h) → k
  17. Intersect(k, h_1) → M, N
  18. Intersect(k, f) → O, P
  19. Polygon(B, N, E) → poly2, e_2, b_1, n_1
  20. Polygon(G, P, E) → poly3, e_3, g_1, p
  21. Polygon(A, M, G) → poly4, g_2, a_2, m
  22. Polygon(A, O, B) → poly5, b_2, a_3, o
  23. Line(L, yAxis) → i
  24. Point(i) → Q
  25. Angle(Q, L, M) → α
  26. Angle(Q, L, O) → β
  27. Angle(P, L, Q) → γ
  28. Angle(N, L, Q) → δ
  29. Rotate(M, -(n * α), L) → M'
  30. Rotate(O, -(n * β), L) → O'
  31. Polygon(A, M', G) → poly6, g_3, a_4, m'
  32. Polygon(O', A, B) → poly7, b_3, o', a_5
  33. Angle(N, B, Q) → ε
  34. Rotate(P, n * γ, L) → P'
  35. Polygon(G, P', E) → poly8, e_4, g_4, p'
  36. Rotate(N, n * δ, L) → N'
  37. Polygon(E, N', B) → poly9, b_4, e_5, n'
  38. Polygon(B, E, N') → poly10, n'_1, b_5, e_6

AI Drawing Prompt Reference

Draw a square-based pyramid. The base is a square with equal sides. Four congruent isosceles triangles form the sides, perpendicular to the base. The vertices of the triangles are above the center of the base. Construct by drawing the square, then the triangles, and finally connecting the vertices to form the pyramid shape.
The prompt above was compiled from the original drawing commands and is for reference only.