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Dynamic Demonstration of the Area of a Trapezium

Dynamic Demonstration of the Area of a Trapezium
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2016-06-07 21:57
PolygonAngleTransformationGeometric Construction
This GeoGebra example dynamically demonstrates the area formula of a trapezium by constructing its vertices, bases, height, and auxiliary points. It covers trapezium area, perpendicular distance, segment length, midpoint, rotation, angle marking, and conditional display. The construction uses Point, Segment, Line, Polygon, Midpoint, OrthogonalLine, Intersect, Rotate, If, and Angle, with text objects showing labels and formula results. Suitable for elementary or middle-school geometry, area-formula teaching, and GeoGebra construction practice.

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
  21. Angle(D, F, A) → β
  22. Midpoint(a_2) → L
  23. Midpoint(h) → M
  24. Segment(A, D) → g
  25. Polygon(A, C, D) → poly1, d_1, a_3, c_1
  26. Polygon(A, D, B) → poly2, b_1, a_4, d_2

AI Drawing Prompt Reference

Please draw a dynamic demonstration of the area formula of a trapezium. First, construct the four vertices A, B, C, D and draw the bases AB and CD. Then, construct a line perpendicular to base CD and find its intersection with base AB, labeled F. Next, mark the height segment AD and calculate its length. Also, construct the midpoint E on the axis of symmetry and rotate the vertices A, C, D, B around E to get A', C', D', B'. In the rotated figure, mark the height segments A'D' and B'C'. Then, mark the vertical distance between the height segment AD and the rotated height segment A'D' and calculate its length. Finally, mark the angle between the height segment AD and the rotated height segment A'D' and display the trapezium area formula.
The prompt above was compiled from the original drawing commands and is for reference only.