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Area of a Trapezoid by yerkin

Area of a Trapezoid by yerkin
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2017-11-07 15:21
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the calculation of a trapezoid's area. Key mathematical concepts include the definition and area formula of a trapezoid. Using GeoGebra commands such as Line, Point, Polygon, Intersect, etc., the area of the trapezoid can be dynamically shown. Suitable for middle school and above students to learn geometric construction and area calculation.

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

AI Drawing Prompt Reference

Draw a trapezoid and calculate its area. First, draw a line a through points A and B, then draw line b through point C and line a. Take points D and E on line b. Use points D, E, F, and A to form trapezoid poly1. Find the midpoint G of the top base, draw line c through points E and G, and it intersects line a at point H. Use points G, D, and E to form triangle poly2. Rotate points G, D, and E to get G', D', and E', and use them to form triangle poly2'. Finally, rotate points G, D, and E to get G'_1, D'_1, and E'_1, and use them to form triangle poly2'_1.
The prompt above was compiled from the original drawing commands and is for reference only.