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Discovering the Area of a Trapezoid

Discovering the Area of a Trapezoid
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2019-04-06 05:29
Coordinate GeometryGeometric Construction
This example demonstrates the process of discovering the formula for the area of a trapezoid through geometric construction. Key mathematical concepts include the properties of trapezoids and area calculation. GeoGebra commands used include line segment construction, distance measurement, points, and polygons. Suitable for middle school and above students learning geometry and area calculation.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Segment(B, A) → i
  4. Distance(A, B) → distanceAB
  5. Line(C, i) → f
  6. Point(f) → D
  7. Segment(C, D) → g
  8. Segment(A, C) → h
  9. Segment(B, D) → j
  10. Midpoint(A, C) → E
  11. Midpoint(B, D) → F
  12. Segment(E, F) → k
  13. Distance(C, D) → distanceCD
  14. Distance(E, F) → distanceEF
  15. Distance(A, B) → a
  16. OrthogonalLine(D, i) → m
  17. Intersect(m, xAxis) → I
  18. Segment(I, D) → n
  19. Distance(D, I) → distanceDI
  20. Point(Circle[G, distanceEF]) → H
  21. Segment(G, H) → l
  22. Point(Circle[J, distanceDI]) → K
  23. Segment(J, K) → p
  24. OrthogonalLine(K, p) → q
  25. OrthogonalLine(H, l) → r
  26. Intersect(q, r) → L
  27. Segment(K, L) → s
  28. Segment(H, L) → t
  29. Polygon(C, D, B, A) → q1, c, d, b, a_1
  30. Intersect(l, t) → M
  31. Intersect(s, t) → N
  32. Intersect(p, s) → O
  33. Polygon(G, M, N, O) → q2, g_1, m_1, n_1, o
  34. PointIn(q1) → Pointq1_1
  35. PointIn(q2) → Pointq2_1
  36. PointIn(q1) → Pointq1_2
  37. PointIn(q1) → Pointq1
  38. PointIn(q2) → Pointq2