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Area of Pentagon with Side Length 7

Area of Pentagon with Side Length 7
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2015-03-22 06:00
PolygonGeometric Construction
This example demonstrates how to calculate the area of a regular pentagon with a side length of 7. Key mathematical concepts include polygon area calculation and geometric construction. Using GeoGebra commands such as Polygon, LineBisector, Intersect, etc., the construction process of the pentagon is visually demonstrated. Suitable for middle school and above students to learn polygon area calculation and geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly1, a_1, b, c, d, e, C, D, E
  2. LineBisector(d) → g
  3. LineBisector(c) → h
  4. Intersect(g, h) → F
  5. Polygon(A, F, B) → poly2, b_1, a_2, f_1
  6. Segment(F, E) → i
  7. Segment(F, D) → j
  8. Segment(F, C) → k
  9. Angle(A, F, B) → α
  10. Segment(A, G) → l
  11. Vector(A, H) → u
  12. Translate(A, u) → A'
  13. Translate(F, u) → F'
  14. Translate(B, u) → B'
  15. Polygon(A', F', B') → poly2', b', a', f'
  16. OrthogonalLine(F', l) → m
  17. Intersect(f, m, 1) → I
  18. Segment(I, F') → n
  19. Angle(H, F', I) → β
  20. Angle(F', I, H) → γ
  21. PointIn(poly2') → Pointpoly2'
  22. PointIn(poly1) → Pointpoly1

AI Drawing Prompt Reference

Draw a regular pentagon with a side length of 7 and calculate its area. Start by using points A and B and the Polygon command to draw the pentagon. Then, find the intersection point F by constructing the angle bisectors of lines CD and CE. Use point F to form a new triangle with points A and B. Next, construct a new pentagon using lines from F to A, B, and C, and calculate its area.
The prompt above was compiled from the original drawing commands and is for reference only.