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Trapezoid Area Calculation by Loizos Loizou

Trapezoid Area Calculation by Loizos Loizou
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2018-01-30 01:47
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the calculation of trapezoid area. Key mathematical concepts include the trapezoid area formula and its application. Using GeoGebra commands such as Point, Segment, Polygon, etc., the construction process of the trapezoid is dynamically shown. Suitable for middle school and above students to learn geometric construction and area calculation.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B_3
  3. Point(yAxis) → C
  4. Segment(A, B_3) → B_1
  5. Line(C, B_1) → b
  6. Point(b) → B
  7. Point(b) → E
  8. Segment(B, E) → c
  9. Segment(B, A) → d
  10. Segment(E, B_3) → e
  11. Midpoint(E, B_3) → F
  12. Ray(B, F) → f
  13. Ray(A, B_3) → g
  14. Intersect(f, g) → G
  15. Polygon(B, E, F) → poly1, f_1, d_1, e_1
  16. Rotate(B, 45°, F) → D'
  17. Rotate(F, 45°, F) → F'
  18. Rotate(B, (-α), F') → Γ
  19. Rotate(E, (-α), F') → E'
  20. Rotate(F, (-α), F') → F'_1
  21. Polygon(Γ, E', F'_1) → poly1', B_2, d'_1, e'
  22. Polygon(B, F'_1, B_3, A) → poly2, d_2, f'_2, b_1, a_1
  23. OrthogonalLine(B, g) → h
  24. Intersect(b_1, h) → H
  25. Segment(B, H) → υ

AI Drawing Prompt Reference

Draw a trapezoid with two parallel bases and two unequal non-parallel sides. Start by creating points A and B_3 on the x-axis, and point C on the y-axis. Connect A and B_3 to form the base B_1. Draw a line b from C, and find the intersection points B and E. Connect BE and EB_3 to form the non-parallel sides. Find the midpoint F of BE, and draw two 45-degree rays f and g from F, intersecting at G. Then, draw a triangle with vertices B, E, and F. Rotate B, E, and F to get new points D', F', and E', and draw two new triangles with these points. Finally, draw a line perpendicular to g from B, intersecting b at H, and connect BH.
The prompt above was compiled from the original drawing commands and is for reference only.