MathPlotAI Logo MathPlotAI

Pyramid Surface Area Calculation by Rasha Tarek

Pyramid Surface Area Calculation by Rasha Tarek
Loading the math board and drawing, please wait…
2015-10-18 09:15
TrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the calculation method for the surface area of a pyramid. It involves core mathematical concepts such as area, polygons, trigonometric functions, and coordinate geometry. Key GeoGebra commands used in construction include Vector, Translate, Segment, Sequence, OrthogonalLine, and Polygon. It is suitable for high school students studying solid geometry.

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