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Area of a 10-gon with Radius r = 4

Area of a 10-gon with Radius r = 4
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2015-03-22 06:46
CirclePolygonCoordinate GeometryTransformationGeometric Construction
This example demonstrates the area calculation of a 10-gon with a radius of 4. Key mathematical concepts include the area of a polygon and geometric construction. Using GeoGebra commands such as Polygon, Vector, LineBisector, Intersect, Translate, Segment, Angle, Circle, OrthogonalLine, and PointIn, a 10-gon is constructed and its area is calculated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 10) → poly1, a_1, k, C, D, E, F, G, H, I, J, b, c, d, e, g, h, i, j
  2. Vector(A, K) → u
  3. LineBisector(i) → l
  4. LineBisector(b) → m
  5. Intersect(l, m) → L
  6. Polygon(A, L, B) → poly2, b_1, a_2, l_1
  7. Translate(A, u) → A'
  8. Translate(L, u) → L'
  9. Translate(B, u) → B'
  10. Polygon(A', L', B') → poly2', b', a', l'
  11. Segment(J, L) → n
  12. Segment(I, L) → p
  13. Segment(H, L) → q
  14. Segment(G, L) → r
  15. Segment(F, L) → s
  16. Segment(E, L) → t
  17. Segment(D, L) → c_1
  18. Segment(C, L) → d_1
  19. Angle(A, L, B) → α
  20. Circle(L, I) → e_1
  21. OrthogonalLine(L', l') → f_1
  22. Intersect(f, f_1, 1) → M
  23. Segment(L', M) → g_1
  24. Angle(K, L', M) → β
  25. Angle(L', M, K) → γ
  26. PointIn(poly1) → Pointpoly1