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Trapezoid Area Proof

Trapezoid Area Proof
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2018-07-12 00:39
VectorCalculusGeometric Construction
This example dynamically demonstrates the proof of the trapezoid area formula. It involves core math concepts like trapezoid, area, vector, rotation, translation, and integral calculus. Construction highlights include using commands like Segment, Line, Point, Midpoint, Vector, Rotate, Translate in GeoGebra. Suitable for high school mathematics education to understand the derivation of the trapezoid area formula.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Line(C, f) → g
  3. Point(g) → D
  4. Segment(C, D) → h
  5. Segment(C, A) → i
  6. Segment(D, B) → j
  7. Midpoint(j) → E
  8. Vector(A, E) → u
  9. Segment(A, F) → k
  10. Rotate(A, ((-w) * π), F) → A'
  11. Rotate(F, ((-w) * π), F) → F'
  12. Segment(A', F') → k'
  13. Translate(A, Vector[(b * Vector[A, D])]) → A'_1
  14. Translate(B, Vector[(b * Vector[A, D])]) → B'
  15. Segment(A'_1, B') → f'