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Area of a Trapezium Finding and Comparing

Area of a Trapezium Finding and Comparing
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2012-05-17 20:37
Geometric Construction
In collections Area, perimeter and volume of shapes Area, Perimeter and Volume of shapes
This example demonstrates how to calculate the area of a trapezium and compare it with other quadrilaterals such as parallelograms, rhombuses, rectangles, and triangles. The key mathematical concepts include the trapezium area formula, methods for calculating areas of various geometric shapes, and principles of comparing geometric figures. Construction involves using GeoGebra commands like Line, OrthogonalLine, Point, Intersect, Polygon, Segment, Angle, Midpoint, and Rotate to create trapeziums and other shapes. Suitable for middle or high school mathematics education to understand area calculations and applications of geometric properties.

GeoGebra Commands & Parameters

  1. Line(A, B) → Lbase
  2. OrthogonalLine(A, Lbase) → Lleft
  3. Point(Lleft) → C
  4. Line(C, Lbase) → Labove
  5. OrthogonalLine(B, Lbase) → Lright
  6. Intersect(Labove, Lright) → D
  7. Point(Lbase) → E
  8. Point(Lbase) → F
  9. Point(Labove) → G
  10. Point(Labove) → H
  11. Polygon(G, E, F, H) → trapezium_1, c, b, d, a
  12. OrthogonalLine(G, Labove) → Lheight
  13. Intersect(Lbase, Lheight) → J
  14. Segment(G, J) → h
  15. Angle(G, E, F) → ε
  16. Angle(E, G, H) → ζ
  17. Angle(G, H, F) → η
  18. Angle(H, F, E) → θ
  19. Polygon(E, G, H, F) → square_1, e, g, h_1, f
  20. Polygon(E, G, H, F) → triangle_1, e_1, g_1, h_2, f_1
  21. Polygon(E, G, H, F) → parallelogram, e_2, g_2, h_3, f_2
  22. Polygon(E, G, H, F) → rectangle_1, e_3, g_3, h_4, f_3
  23. Polygon(E, G, H, F) → rhombus, e_4, g_4, h_5, f_4
  24. Segment(J, E) → i
  25. Midpoint(H, F) → I
  26. Rotate(E, -α, I) → Er
  27. Rotate(G, -α, I) → Gr
  28. Rotate(F, -α, I) → Fr
  29. Rotate(H, -α, I) → Hr
  30. Polygon(Er, Fr, Hr, Gr) → mirror, b', fr, a', gr
  31. Angle(Hr, Fr, Er) → β
  32. Angle(Fr, Er, Gr) → γ
  33. Angle(Er, Gr, Hr) → δ
  34. Angle(Gr, Hr, Fr) → ι