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Areas of Quadrilaterals and Triangles

Areas of Quadrilaterals and Triangles
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2014-11-24 19:07
PolygonAngleGeometric Construction
This example demonstrates how to calculate the areas of quadrilaterals and triangles using geometric construction methods. Key mathematical concepts include area calculation, properties of triangles and quadrilaterals. It utilizes commands such as Polygon, PointIn, Line, AngularBisector, Segment, Intersect in GeoGebra. Suitable for middle school and above students to learn geometric construction and area calculation.

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, and let them intersect at points F and E. Connect A, B, C, and D to form quadrilateral ABCD, connect B, C, D, and E to form quadrilateral BCDE, and connect A, E, F, and D to form quadrilateral AEDF.
The prompt above was compiled from the original drawing commands and is for reference only.