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Area of a Trapezium by croober

Area of a Trapezium by croober
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2015-06-09 07:07
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the calculation of a trapezium's area. Key mathematical concepts include the properties and area formula of a trapezium. Using GeoGebra commands such as Line, Segment, Point, and Polygon, the construction process of a trapezium is dynamically shown. Suitable for middle school and above students to learn geometric construction and area calculation.

GeoGebra Commands & Parameters

  1. Line(A, D) → a
  2. Line(C_1, a) → b
  3. Segment(A, D) → c
  4. Segment(A, C_1) → d
  5. Point(b) → D_1
  6. Segment(D, D_1) → e
  7. Segment(C_1, D_1) → f
  8. Midpoint(d) → E
  9. Midpoint(e) → F
  10. Polygon(A, E, F, D) → poly1, a_1, e_1, f_1, b_1
  11. Polygon(E, C_1, D_1, F) → poly2, e_2, c_1, d_1, f_2
  12. Rotate(E, -(Rotate), F) → E'
  13. Rotate(C_1, -(Rotate), F) → B
  14. Rotate(D_1, -(Rotate), F) → C
  15. Rotate(F, -(Rotate), F) → F'
  16. Polygon(E', B, C, F') → poly2', e', c', d', f'
  17. Midpoint(c) → G
  18. Midpoint(c') → H
  19. Point(poly2) → I
  20. OrthogonalLine(I, c_1) → g
  21. Intersect(g, c) → J
  22. Segment(I, J) → h
  23. Midpoint(h) → K
  24. Midpoint(J, K) → L
  25. Segment(J, K) → i

AI Drawing Prompt Reference

Draw a trapezium with two parallel line segments AD and C1D1, and two perpendicular line segments AC1 and AD1. Construct the height of the trapezium using midpoints and rotations, then draw two rectangles to calculate the trapezium's area.
The prompt above was compiled from the original drawing commands and is for reference only.