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Trapezoid Area Calculation by Jeff Caldwell

Trapezoid Area Calculation by Jeff Caldwell
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2017-08-18 04:16
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to dynamically calculate the area of a trapezoid. It involves core mathematical concepts like trapezoid definition, area formula, midpoint, rotation, orthogonal line, intersection calculation. Construction highlights include using commands like Segment, Line, Point, Polygon, Midpoint, Rotate, OrthogonalLine, Intersect, If to build the trapezoid and calculate height. Suitable for middle school and above students to learn geometric area calculation methods.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a_2
  2. Line(C, a_2) → b_2
  3. Point(b_2) → D
  4. Polygon(A, C, D, B) → P, a_1, a, d, b
  5. Midpoint(D, B) → E
  6. Rotate(A, (-rotate), E) → A'
  7. Rotate(C, (-rotate), E) → C'
  8. Rotate(D, (-rotate), E) → D'
  9. Rotate(B, (-rotate), E) → B'
  10. Polygon(A', C', D', B') → P', a', c', d', b'
  11. Line(A, B) → e
  12. OrthogonalLine(D, e) → f
  13. Intersect(f, e) → F
  14. Segment(A, F) → c
  15. Midpoint(B', A') → G
  16. Midpoint(D', C') → H
  17. If(rotate ≥ 0°, H) → I
  18. If(rotate > 0°, H) → J
  19. If(rotate > 0°, G) → K
  20. Segment(D, F) → h_1
  21. Angle(D, F, A) → β
  22. Midpoint(a_2) → L
  23. Midpoint(h_1) → M
  24. Segment(A, D) → g
  25. Polygon(A, C, D) → h_2, d_1, a_3, c_1
  26. Polygon(A, D, B) → poly2, b_1, a_4, d_2
  27. Line(D, C) → i
  28. OrthogonalLine(A, i) → j
  29. Intersect(i, j) → N
  30. Segment(N, C) → k
  31. Segment(A, N) → h
  32. Intersect(h, k) → O
  33. Angle(A, O, D) → α

AI Drawing Prompt Reference

Draw a trapezoid ABCD with A and B as the endpoints of the longer base and C and D as the endpoints of the shorter base. Rotate the trapezoid to create two new trapezoids A'B'C'D' and A''B''C''D''. Then, draw the perpendicular bisector of AB, intersecting AB at point F. Next, draw the perpendicular bisector of CD, intersecting CD at point N. Finally, draw line segment h through points A and N, intersecting line segment k at point O, and calculate the height and area of the trapezoid.
The prompt above was compiled from the original drawing commands and is for reference only.