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Area and Construction of an Equilateral Triangle

Area and Construction of an Equilateral Triangle
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2018-05-11 14:06
TriangleTrigonometryGeometric Construction
This example demonstrates the calculation of the area and geometric construction of an equilateral triangle. Key math concepts include properties of equilateral triangles, area formulas, cosine theorem, centroid, etc. Construction highlights the use of GeoGebra commands and objects like Point, Segment, OrthogonalLine, Rotate, Angle, Ray, Intersect, Textfield, Polygon, Area, Circle. Suitable for high school students learning geometric constructions and area calculations.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → ऊँचाई
  3. OrthogonalLine(A, ऊँचाई) → c
  4. Rotate(A, 30°, B) → A'
  5. Angle(A, B, A') → α
  6. Ray(B, A') → d
  7. Intersect(c, d) → C
  8. Segment(B, C) → e
  9. Rotate(A, 330°, B) → A'_1
  10. Angle(A'_1, B, A) → β
  11. Ray(B, A'_1) → f
  12. Intersect(c, f) → D
  13. Segment(B, D) → g
  14. Segment(D, C) → h
  15. Angle(C, A, B) → γ
  16. Angle(A, D, B) → δ
  17. Angle(B, C, A) → ε
  18. Textfield(a) → inputBox1
  19. Polygon(B, D, C) → poly1, c_1, b_1, d_1
  20. Area(B, D, C) → i
  21. Circle(D, (0.75 * a)) → k
  22. Circle(C, (0.75 * a)) → p

AI Drawing Prompt Reference

Draw an equilateral triangle, showing its height and the perpendicular line from a vertex to the opposite side. From the midpoint of one side, draw two rays rotated by 30° and 330°, intersecting the perpendicular line to find the other two vertices, completing the triangle. Label the side length, calculate the area, and draw circles centered at two vertices with radii 0.75 times the side length.
The prompt above was compiled from the original drawing commands and is for reference only.