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Calculating Areas of Quadrilaterals

Calculating Areas of Quadrilaterals
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2014-11-12 16:16
Coordinate GeometryIntegralGeometric Construction
This example demonstrates how to calculate the area of a quadrilateral using coordinates. It involves core math concepts like coordinate geometry, line segments, angles, and definite integrals. Construction highlights include commands like Polygon, PointIn, Line, AngularBisector, Segment, Intersect, Corner, Angle, OrthogonalLine. Suitable for high school geometry instruction and construction learning.

GeoGebra Commands & Parameters

  1. Polygon(J, K, L, M) → poly2, j_1, k_1, l_1, m_1
  2. PointIn(poly2) → N
  3. Line(A, D) → l
  4. PointIn(poly2) → B
  5. AngularBisector(B, A, D) → d
  6. Segment(D_1, E_1) → e
  7. Intersect(e, d) → F_1
  8. AngularBisector(D, A, B) → k
  9. Corner(1, 1) → Cnr1
  10. Corner(1, 2) → Cnr2
  11. Corner(1, 3) → Cnr3
  12. Corner(1, 4) → Cnr4
  13. Polygon(CN1, CN2, CN3, CN4) → Panel, cn1, cn2, cn3, cn4
  14. Angle(B, D, A) → γ
  15. Angle(A, B, D) → ε
  16. Line(B, l) → a
  17. OrthogonalLine(A, l) → b
  18. Intersect(a, b) → E
  19. OrthogonalLine(D, l) → c
  20. Intersect(a, c) → F
  21. Segment(A, B) → f
  22. Line(D, f) → g
  23. Intersect(a, g) → C
  24. Segment(E, F) → h
  25. Segment(B, C) → i
  26. Segment(D, F) → m
  27. Segment(A, E) → n
  28. Segment(A, D) → p
  29. Angle(F, D, A) → α
  30. Angle(A, E, F) → β
  31. Segment(D, C) → j
  32. Polygon(A, E, F, D) → poly1, a_1, g_1, h_1, c_1
  33. Polygon(A, B, C, D) → poly3, a_2, b_1, i_1, c_2
  34. Polygon(A, B, D) → poly4, c_3, a_3, b_2

AI Drawing Prompt Reference

Draw a quadrilateral ABCD, then select a point N inside it. Draw the perpendicular bisectors of AD and BC, which intersect at point F. Draw the perpendicular bisectors of AB and CD, which intersect at point E. Connect A, B, C, and D to form quadrilateral ABCD. Then draw the diagonals AC and BD of quadrilateral ABCD, which intersect at point F. Finally, draw quadrilaterals ABEF and ACDF.
The prompt above was compiled from the original drawing commands and is for reference only.