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Area of Square and Triangle

Area of Square and Triangle
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2017-04-13 06:54
TrianglePolygonGeometric Construction
This example demonstrates the calculation of the area of a square and a triangle. Key mathematical concepts include area formulas and properties of similar triangles. Geometric construction is carried out using GeoGebra commands such as Intersect, Point, and Polygon. Suitable for students in middle school and above to learn about area calculation and similar triangles.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Semicircle(A, B) → c
  5. Segment(D, B) → j
  6. Tangent(C, c) → k, p
  7. Intersect(c, k, 1) → E
  8. Segment(E, B) → l
  9. Intersect(c, j, 2) → F
  10. Segment(E, F) → m
  11. Segment(E, C) → n
  12. Polygon(E, F, B) → poly2, b, e, f_1
  13. Line(E, j) → q
  14. Intersect(f, q) → G
  15. If(1 ≤ a < 2, Polygon[F, Dilate[E, 2 - a, G], B], Polygon[F, G, B]) → poly3
  16. Midpoint(g) → H
  17. If(3 ≤ a < 4, Polygon[G, Dilate[F, 4 - a, H], B], Polygon[H, G, B]) → poly4
  18. Midpoint(G, B) → I
  19. If(5 ≤ a < 6, Segment[B, Dilate[B, 6 - a, I]], Segment[B, I]) → r
  20. If(5 ≤ a < 6, Segment[B, Dilate[B, 6 - a, H]], Segment[B, H]) → s
  21. If(7 ≤ a < 8, Rotate[r, ((-(a - 7)) * π), I], Segment[G, I]) → t
  22. If(7 ≤ a < 8, Rotate[s, ((a - 7) * π), H], Segment[H, C]) → d
  23. If(9 ≤ a < 10, Polygon[B, Dilate[G, 10 - a, I], Dilate[H, 10 - a, C]], Polygon[I, B, C]) → poly5
  24. If(11 ≤ a < 12, Rotate[poly5, ((a - 11) * π), Midpoint[I, C]], Rotate[poly5, ((12 - 11) * π), Midpoint[I, C]]) → poly6
  25. If(13 ≤ a < 14, Translate[{poly5, poly6}, Vector[((a - 13) * Vector[B, I])]], Translate[{poly5, poly6}, Vector[B, I]]) → list1
  26. If(13 ≤ a < 14, Translate[{poly5, poly6}, Vector[((2 * (a - 13)) * Vector[B, I])]], Translate[{poly5, poly6}, Vector[(2 * Vector[B, I])]]) → list2
  27. If(13 ≤ a < 14, Translate[{poly5, poly6}, Vector[((3 * (a - 13)) * Vector[B, I])]], Translate[{poly5, poly6}, Vector[(3 * Vector[B, I])]]) → list3
  28. If(13 ≤ a < 14, Translate[{poly5, poly6}, Vector[((4 * (a - 13)) * Vector[B, I])]], Translate[{poly5, poly6}, Vector[(4 * Vector[B, I])]]) → list4
  29. OrthogonalLine(F, i) → g_1