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Pyramid Surface Area Demonstration

Pyramid Surface Area Demonstration
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2019-05-08 02:32
VectorCoordinate GeometrySolid Geometry
This example demonstrates the calculation of a pyramid's surface area. Key mathematical concepts include solid geometry surface area calculations. Using vector, polygon, and coordinate geometry commands, users can dynamically explore the pyramid's faces and calculate its surface area. Suitable for high school geometry education and teaching.

GeoGebra Commands & Parameters

  1. Vector(B_1, Y) → u
  2. Vector(B_1, Z) → v
  3. Vector(B_1, X) → w
  4. Translate(O, Vector[(h * w)]) → S
  5. Vector(S, O) → z
  6. Translate(S, Vector[(sin(k°) * z)]) → S'
  7. Segment(O, S) → l
  8. Sequence((x(O), y(O)) - (r * (((sin(0°) * sin(i°)) * v) + ((cos(0°) * sin(i°)) * v) - (cos(i°) * u))), i, 0, k_2, k_2 / Faces) → liste1
  9. Segment(Element[liste1, 1], S) → j
  10. OrthogonalLine(View3D, yAxis) → a
  11. OrthogonalLine(View3D, xAxis) → b
  12. Translate(O, w) → O'_1
  13. Segment(Element[liste1, 1], S) → d
  14. Sequence(Segment[Element[liste1, i], S], i, 1, Faces) → liste4
  15. Sequence(Segment[Element[liste1, i], Element[liste1, i + 1]], i, 1, Faces) → liste3
  16. Translate(O, Vector[(f * v)]) → R
  17. Sequence((x(S'), y(S')) - (aa * (((sin(k°) * sin(i°)) * v) + ((cos(k°) * sin(i°)) * v) - (cos(i°) * u))), i, 0, k_2, k_2 / Faces) → liste6
  18. Segment(Element[liste1, 1], Element[liste1, 2]) → m
  19. Segment(Element[liste1, 2], S) → q
  20. Segment(Element[liste1, 2], O) → c_1
  21. Sequence(Midpoint[Element[liste6, i], Element[liste6, i + 1]], i, 0, Faces) → liste7
  22. Sequence(Polygon[Element[liste1, i], Element[liste1, i + 1], S], i, 0, Faces) → liste8
  23. Sequence(Polygon[Element[liste1, i], Element[liste1, i + 1], O], i, 0, Faces) → liste11
  24. Polygon(O, Element[liste1, 1], Element[liste1, 2]) → poly1, d_1, e_1, f_1
  25. Sequence(Polygon[Element[liste1, i], Element[liste1, i + 1], Element[liste7, i + 1]], i, 0, Faces) → liste10
  26. Sequence(Polygon[Element[liste1, i], Element[liste1, i + 1], Element[liste7, i + 1]], i, 0, Faces) → liste2