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Equal Area Triangle and Rectangle

Equal Area Triangle and Rectangle
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2015-10-14 01:16
TriangleGeometric ConstructionSlider AnimationGraphing
In collections Perimeters vs. Areas
This example demonstrates the relationship between the areas of a triangle and a rectangle that are equal. Key mathematical concepts include the calculation of a triangle's area and the conditions for equal areas. By dragging points A, B, and C to change the triangle, point R can adjust the rectangle's size while keeping its area equal to that of the triangle. The construction uses commands such as Polygon, Circle, Point, Ray, OrthogonalLine, Distance, Intersect, Segment, Angle, and Line. Suitable for middle school and above students to learn geometric transformations and area calculations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Circle(D, Area[poly1]) → d
  3. Point(d) → E
  4. Ray(D, E) → e
  5. Point(e) → R
  6. OrthogonalLine(R, e) → f
  7. Distance(D, R) → w
  8. Circle(R, h) → k
  9. Intersect(k, f, 2) → G
  10. OrthogonalLine(G, f) → g
  11. OrthogonalLine(D, g) → i
  12. Intersect(g, i) → H
  13. Polygon(D, R, G, H) → poly2, d_1, f_1, g_1, h_1
  14. Point(yAxis) → F
  15. Point(yAxis) → I
  16. Point(Circle[I, a]) → J
  17. Segment(I, J) → j
  18. Point(Circle[J, b]) → K
  19. Segment(J, K) → l
  20. Point(Circle[K, c]) → L
  21. Segment(K, L) → m
  22. Point(Circle[F, d_1]) → M
  23. Segment(F, M) → n
  24. Point(Circle[M, f_1]) → N
  25. Segment(M, N) → p
  26. Point(Circle[N, g_1]) → O
  27. Segment(N, O) → q
  28. Point(Circle[O, h_1]) → P
  29. Segment(O, P) → r
  30. Circle(A, b) → s
  31. Circle(C, b) → t
  32. Intersect(s, t, 1) → Q
  33. Intersect(s, t, 2) → S
  34. OrthogonalLine(C, b) → a_1
  35. Circle(C, b) → c_1
  36. Intersect(c_1, a_1, 2) → T
  37. Intersect(c_1, a_1, 1) → U
  38. Angle(A, C, B) → α
  39. OrthogonalLine(B, a_1) → b_1
  40. Intersect(a_1, b_1) → projB
  41. Line(Q, S) → e_1
  42. Intersect(b_1, e_1) → V
  43. Circle(A, sqrt((Area[poly1] * 4 / sqrt(3)))) → k_1