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Derive Area of Regular Polygons

Derive Area of Regular Polygons
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2017-03-15 04:25
PolygonAngleGeometric Construction
This example demonstrates how to derive the area formula for regular polygons. Key mathematical concepts include polygons, triangles, and angles. Using GeoGebra commands such as Random, Point, Midpoint, Rotate, etc., the construction of regular polygons and the derivation of their area are illustrated. Suitable for middle school and above students to learn geometric construction and area calculation.

GeoGebra Commands & Parameters

  1. Random(3, 9) → p
  2. Random(100, 500) → a
  3. Point(Circle[A, b]) → B
  4. Midpoint(A, B) → I
  5. Rotate(A, (-(c°)), B) → A'
  6. Line(B, A') → q
  7. Rotate(B, c°, A) → B'
  8. Line(A, B') → n
  9. Intersect(n, q) → H
  10. Segment(H, I) → s
  11. Segment(A, B) → f
  12. Polygon(A, B, p) → poly1, g, C, D, E, F, G, J, K, h, i, j, k, l, m, t, d
  13. Angle(B, A, B') → α
  14. Angle(A', B, A) → β
  15. Segment(A, H) → r
  16. Sequence(Segment[Rotate[A, ((360 * t / p))°, H], Rotate[H, ((360 * t / p))°, H]], t, 1, p) → list1
  17. Angle(H, I, B) → γ
  18. Polygon(A, B, H) → poly2, h_1, a_1, b_1
  19. Textfield(tn) → InputBox2
  20. Textfield(ta) → InputBox1
  21. Textfield(ra) → InputBox3