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Fixed Area Geometric Shapes

Fixed Area Geometric Shapes
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2015-10-12 00:01
PolygonTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to construct various geometric shapes like kites, rectangles, squares, and trapezoids with a fixed area using GeoGebra. It involves core concepts such as area calculation, geometric construction, trigonometric functions, and arithmetic mean. Key GeoGebra commands and objects used include Line, OrthogonalLine, Circle, Intersect, Polygon, Point, Segment, Semicircle, and Mirror. Suitable for high school mathematics education to understand the properties and area relationships of geometric figures.

GeoGebra Commands & Parameters

  1. Textfield(area2be) → InputBox1
  2. Line(A, B) → a
  3. OrthogonalLine(A, a) → b
  4. Circle(A, area2be / Distance[A, B]) → c
  5. Intersect(c, b, 2) → C
  6. Polygon(B, A, C, D) → poly1, b_1, a_1, c_1, d
  7. Line(E, a) → e
  8. Point(e) → F
  9. Polygon(A, B, F) → poly2, f, a_2, b_2
  10. Line(C, a) → i
  11. Point(i) → G
  12. Polygon(G, H, B, A) → poly3, g_1, h_1, b_3, a_3
  13. Segment(F, Intersect[a, OrthogonalLine[F, a]]) → k
  14. Segment(G, Intersect[a, OrthogonalLine[G, a]]) → l
  15. Polygon(I, A, B, J) → poly4, i_1, a_4, b_4, j_1
  16. Segment(I, Intersect[a, OrthogonalLine[I, a]]) → m
  17. Semicircle(A, B) → p
  18. Circle(A, area2be / ((2 * Distance[A, B]))) → q
  19. Intersect(q, b, 2) → K
  20. Intersect(p, OrthogonalLine[K, b]) → L, M
  21. Mirror(B, M) → B'
  22. Mirror(A, M) → A'
  23. Polygon(B, A, B', A') → poly5, b_5, a_5, b', a'
  24. Segment(B, B') → r
  25. Segment(A, A') → s
  26. Point(p) → N
  27. Mirror(A, N) → A'_1
  28. Polygon(B, A'_1, O, A) → poly6, b_6, a'_1, o_1, a_6
  29. Segment(B, O) → t
  30. Segment(A, A'_1) → d_1