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Mr. Smith's: Heptagon Area, Radius r=8.07

Mr. Smith's: Heptagon Area, Radius r=8.07
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2015-03-22 07:00
PolygonTrigonometryCalculus
This example demonstrates how to calculate the area of a heptagon with a radius of 8.07. Key mathematical concepts include polygon area calculation and trigonometric functions. Using GeoGebra commands such as Polygon, LineBisector, Intersect, etc., a heptagon is constructed and its area is calculated. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 7) → poly1, b, E, F, G, c, d, e, g, h, i, C, D
  2. LineBisector(g) → j
  3. LineBisector(e) → k
  4. Intersect(j, k) → H
  5. Polygon(H, B, A) → poly2, a_1, h_1, b_1
  6. Segment(G, H) → l
  7. Vector(A, I) → u
  8. Translate(H, u) → H'
  9. Translate(B, u) → B'
  10. Translate(A, u) → A'
  11. Polygon(H', B', A') → poly2', a', h', b'
  12. Circle(H, G) → p
  13. Segment(G, H) → m
  14. Segment(F, H) → q
  15. Segment(E, H) → r
  16. Segment(D, H) → s
  17. Segment(C, H) → t
  18. OrthogonalLine(H', h') → c_1
  19. Intersect(f, c_1, 1) → J
  20. Segment(H', J) → d_1
  21. Angle(I, H', J) → α
  22. Angle(H', J, I) → β
  23. PointIn(poly1) → Pointpoly1
  24. Angle(A, H, B) → γ