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Area of a Rhombus

Area of a Rhombus
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2023-03-13 04:03
PolygonCalculusGeometric Construction
In collections geometriadinamica.es
This example demonstrates how to calculate the area of a rhombus. It involves the core geometric concept of calculating the area of a rhombus. The example uses GeoGebra commands and objects, including Segment, Line, Intersect, Polygon, OrthogonalLine, Circle, Vector, and Translate. This example is suitable for middle school or high school students learning how to calculate the area of a rhombus.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(A, C) → b
  3. Line(C, a) → c
  4. Line(B, b) → d
  5. Intersect(d, c) → D
  6. Polygon(A, C, D, B) → P, a_1, c_1, d_1, b_1
  7. OrthogonalLine(C, a) → e
  8. Intersect(e, b_1) → E
  9. Polygon(C, E, A) → Q, a_2, c_2, e_1
  10. Circle(A, g) → h
  11. Intersect(h, b_1) → F, G
  12. Vector(A, F) → u
  13. Translate(C, u) → C'
  14. Translate(E, u) → E'
  15. Translate(A, u) → A'
  16. Polygon(C', E', A') → Q', a', c', e'
  17. Polygon(C, E, B, D) → R, c_3, e_2, b_2, d_2
  18. OrthogonalLine(D, b_1) → i
  19. Intersect(b_1, i) → H
  20. Polygon(C, D, H, A) → S, c_4, d_3, h_1, a_3
  21. Polygon(D, H, B) → T, b_3, d_4, h_2
  22. Translate(D, Vector[(-u)]) → D'
  23. Translate(H, Vector[(-u)]) → H'
  24. Translate(B, Vector[(-u)]) → B'
  25. Polygon(D', H', B') → T', b', d', h'

AI Drawing Prompt Reference

Draw a rhombus with vertices formed by two intersecting segments and their parallels. From one vertex, drop a perpendicular to the opposite side, marking the foot on the side, creating a small right triangle. Draw a circle centered at the rhombus center intersecting a side at two points. Translate the small triangle by the vector from the center to one intersection point, placing a congruent triangle on the opposite side. Then connect the diagonal intersection to vertices to form two smaller triangles, and translate one of them in the opposite direction, illustrating how the rhombus area can be decomposed and rearranged.
The prompt above was compiled from the original drawing commands and is for reference only.