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Calculating Polygon Area: Geometric Construction and Area Calculation by tawkac

Calculating Polygon Area: Geometric Construction and Area Calculation by tawkac
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2019-04-02 01:08
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the area of a polygon through geometric construction. The key mathematical concepts include polygon area formulas, geometric transformations, and coordinate geometry. Construction involves using GeoGebra commands such as Intersect, Rotate, Polygon, etc. to create polygon objects. Suitable for middle or high school mathematics learning to understand area calculation and applications of geometric transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → C
  3. Point(xAxis) → F
  4. Rotate(A, ((-(180°)) * t1), D) → A'
  5. Rotate(D, ((-(180°)) * t2), D) → D'
  6. Rotate(F, ((-(180°)) * t1), D) → F'
  7. Polygon(A', D', F') → poly1, f', a', d'
  8. Rotate(D, (180° * t1), D) → D'_1
  9. Rotate(E, (180° * t2), D) → E'
  10. Rotate(B, (180° * t2), D) → B'
  11. Polygon(B', D'_1, E') → poly2, e', b', d'_1
  12. Polygon(C, E, D, F) → poly3, c, e, d, f
  13. Polygon(A', D', F') → poly1', f'_1, a'_1, d'_2
  14. Polygon(B', D'_1, E') → poly2', e'_1, b'_1, d'_3
  15. Polygon(A, B, C) → poly4, c_1, a, b
  16. Polygon(A, F, D, E, B) → poly5, a_1, f_1, d_1, e_1, b_1
  17. Segment(X0, X0 + (0, 0.25)) → g
  18. Segment(X0, X0 + (0, mark)) → h
  19. Segment(X0 + (1, 0), X0 + (1, mark)) → i
  20. Vector(X0 + (0, mark / 2), X0 + (1, mark / 2)) → u
  21. Vector(X0 + (1, mark / 2), X0 + (0, mark / 2)) → v
  22. Segment(Y0 - (mark, 0), Y0) → j
  23. Segment(Y0 - (mark, 1), Y0 - (0, 1)) → k
  24. Vector(Y0 - (mark / 2, 1), Y0 - (mark / 2, 0)) → w
  25. Vector(Y0 - (mark / 2, 0), Y0 - (mark / 2, 1)) → z
  26. Segment((3, -1), (3, 3)) → l