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Calculating Area of a Trapezoid

Calculating Area of a Trapezoid
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2014-12-20 10:48
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to dynamically calculate the area of a trapezoid through geometric constructions. Key math concepts include trapezoid definitions, area formulas, and coordinate geometry. Construction highlights involve commands like Line, Point, Polygon, Midpoint, Intersect, and Rotate to build the trapezoid and auxiliary shapes. Suitable for middle school students and above learning geometric constructions and area calculations, as well as high school coordinate geometry instruction.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(C, a) → b
  3. Point(b) → D
  4. Point(b) → E
  5. Point(a) → F
  6. Polygon(D, E, F, A) → poly1, d, e, f, a_1
  7. Midpoint(A, D) → G
  8. Line(E, G) → c
  9. Intersect(a, c) → H
  10. Polygon(G, D, E) → poly2, e_1, g, d_1
  11. Rotate(G, (-α), G) → G'
  12. Rotate(D, (-α), G) → D'
  13. Rotate(E, (-α), G) → E'
  14. Polygon(G', D', E') → poly2', e', g', d'
  15. Rotate(G, (-α), G) → G'_1
  16. Rotate(D, (-α), G) → D'_1
  17. Rotate(E, (-α), G) → E'_1
  18. Polygon(G'_1, D'_1, E'_1) → poly2'_1, e'_1, g'_1, d'_1