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Area of 15-gon with Perimeter P=180

Area of 15-gon with Perimeter P=180
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2019-04-23 10:33
PolygonGeometric Construction
This example demonstrates the area calculation of a 15-gon with a fixed perimeter of 180. Key mathematical concepts include the area and perimeter of polygons. The construction uses GeoGebra commands such as Intersect, Point, Vector, Polygon, etc. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Vector(A, C) → u
  4. Polygon(A, B, 15) → poly1, b, l, m, n, p, q, r, D, E, F, G, c, H, I, J, K, L, M, N, O, P, d, e, g, h, i, j, k
  5. LineBisector(l) → s
  6. LineBisector(g) → t
  7. Intersect(s, t) → Q
  8. Polygon(A, Q, B) → poly2, b_1, a_1, q_1
  9. Segment(P, Q) → c_1
  10. Segment(O, Q) → d_1
  11. Segment(N, Q) → e_1
  12. Segment(M, Q) → f_1
  13. Segment(L, Q) → g_1
  14. Segment(K, Q) → h_1
  15. Segment(J, Q) → i_1
  16. Segment(I, Q) → j_1
  17. Segment(H, Q) → k_1
  18. Segment(G, Q) → l_1
  19. Segment(F, Q) → m_1
  20. Segment(E, Q) → n_1
  21. Segment(D, Q) → p_1
  22. Translate(A, u) → A'
  23. Translate(Q, u) → Q'
  24. Translate(B, u) → B'
  25. Polygon(A', Q', B') → poly2', b', a', q'
  26. Angle(A, Q, B) → α
  27. OrthogonalLine(Q', q') → r_1
  28. Intersect(f, r_1, 1) → R
  29. Segment(Q', R) → s_1
  30. Angle(C, Q', R) → β
  31. Angle(Q', R, C) → γ
  32. PointIn(poly1) → Pointpoly1