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Trapezium Area Calculation by Mrs Rouse

Trapezium Area Calculation by Mrs Rouse
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2018-06-20 19:12
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the area of a trapezium using coordinate geometry methods. Core math concepts include coordinate geometry, polygon area formulas, midpoint, rotation, orthogonal lines, etc. GeoGebra commands and objects like Segment, Line, Point, Polygon, Midpoint, Rotate, OrthogonalLine, Intersect, If are used in the construction. Suitable for high school mathematics teaching to understand and apply the trapezium area formula.

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