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Area of a Regular Triangle

Area of a Regular Triangle
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2015-03-22 04:03
TriangleCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the area of a regular triangle by constructing angle bisectors and intersection points. Core math concepts include properties of regular triangles, angle bisector theorem, and analytical geometry construction. GeoGebra commands and objects used in the construction are Polygon, LineBisector, Intersect, Segment, Point, Vector, Translate, OrthogonalLine, Angle. Suitable for high school mathematics education, helping students understand the calculation method and geometric construction techniques for regular triangle areas.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. LineBisector(c) → d
  3. LineBisector(a) → e
  4. Intersect(d, e) → D
  5. Polygon(A, D, B) → poly2, b_1, a_1, d_1
  6. Segment(D, C) → f
  7. Point(xAxis) → E
  8. Vector(A, E) → u
  9. Translate(A, u) → A'
  10. Translate(D, u) → D'
  11. Translate(B, u) → B'
  12. Polygon(A', D', B') → poly2', b', a', d'
  13. OrthogonalLine(D', d') → g
  14. Intersect(g, d') → F
  15. Segment(F, D') → h
  16. Angle(A, D, B) → α
  17. Angle(D', F, E) → β
  18. Angle(E, D', F) → γ
  19. Angle(F, E, D') → δ