Measure the Area of a Polygon

Measure the Area of a Polygon
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2019-04-02 01:10
This example demonstrates how to measure the area of a polygon using GeoGebra. Key mathematical concepts include area calculation and geometric construction. Using commands such as Segment, Vector, Point, Translate, and Polygon, a polygon is constructed and its area is measured. Suitable for middle school and above students or teachers for teaching purposes.

GeoGebra Commands & Parameters

  1. Segment(X0, X0 + (0, 0.25)) → g
  2. Segment(X0, X0 + (0, mark)) → h
  3. Segment(X0 + (1, 0), X0 + (1, mark)) → i
  4. Vector(X0 + (0, mark / 2), X0 + (1, mark / 2)) → u
  5. Vector(X0 + (1, mark / 2), X0 + (0, mark / 2)) → v
  6. Segment(Y0 - (mark, 0), Y0) → j
  7. Segment(Y0 - (mark, 1), Y0 - (0, 1)) → k
  8. Vector(Y0 - (mark / 2, 1), Y0 - (mark / 2, 0)) → w
  9. Vector(Y0 - (mark / 2, 0), Y0 - (mark / 2, 1)) → z
  10. Point(yAxis) → A
  11. Point(xAxis) → D
  12. Translate(A, Vector[(t1 * Vector[A, D])]) → A'
  13. Translate(F, Vector[(t1 * Vector[A, D])]) → F'
  14. Translate(B, Vector[(t1 * Vector[A, D])]) → B'
  15. Polygon(A', F', B') → poly1, b', a', f'
  16. Translate(C, Vector[(t2 * Vector[D, A])]) → C'
  17. Translate(D, Vector[(t2 * Vector[D, A])]) → D'
  18. Translate(H, Vector[(t2 * Vector[D, A])]) → H'
  19. Translate(E, Vector[(t2 * Vector[D, A])]) → E'
  20. Polygon(C', D', H') → poly2, a, b, c
  21. Translate(B, Vector[(t3 * Vector[B, A])]) → B'_1
  22. Translate(C, Vector[(t3 * Vector[B, A])]) → C'_1
  23. Translate(E, Vector[(t3 * Vector[B, A])]) → E'_1
  24. Polygon(B'_1, C'_1, E'_1) → poly3, e'_1, b'_1, c'_1
  25. Translate(A, Vector[(t4 * Vector[A, B])]) → A'_1
  26. Translate(G, Vector[(t4 * Vector[A, B])]) → G'
  27. Translate(D, Vector[(t4 * Vector[A, B])]) → D'_1
  28. Polygon(A'_1, G', D'_1) → poly4, d'_1, a'_1, g'
  29. Polygon(E, F, G, H) → poly5, e, f, g_1, h_1
  30. Polygon(A', F', B') → poly1', b'_2, a'_2, f'_1
  31. Polygon(C', D', H') → poly2', d, l, m
  32. Polygon(B'_1, C'_1, E'_1) → poly3', e'_2, b'_3, c'_2
  33. Polygon(A'_1, G', D'_1) → poly4', d'_2, a'_3, g'_1
  34. Polygon(A, B, C, D) → poly6, a_1, b_1, c_1, d_1
  35. Polygon(A, B, F) → poly7, f_1, a_2, b_2
  36. Polygon(B, C, E) → poly8, e_1, b_3, c_2
  37. Polygon(C, D, H) → poly9, h_2, c_3, d_2
  38. Polygon(A, G, D) → poly10, d_3, a_3, g_2

AI Drawing Prompt Reference

Draw a quadrilateral ABCD, then construct a pentagon EFGHI inside it. Next, construct four new polygons from each vertex of the quadrilateral, extending outward, with each polygon overlapping parts of the quadrilateral and pentagon. Finally, measure and display the area of each polygon.
The prompt above was compiled from the original drawing commands and is for reference only.