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Surface Area of a Pyramid

Surface Area of a Pyramid
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2020-04-06 00:58
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the surface area calculation of a pyramid. Key mathematical concepts include the surface area formula for a pyramid in solid geometry. Using GeoGebra commands such as Vector, Translate, Segment, and Polygon, the example dynamically shows the pyramid's faces. Suitable for high school mathematics education and learning.

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

AI Drawing Prompt Reference

Draw a pyramid with a base and four triangular faces. Start by defining the base center point O and the apex S, then construct the pyramid's sides using triangles and polygons to connect the vertices, and finally display the pyramid's surface area.
The prompt above was compiled from the original drawing commands and is for reference only.