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Trapezoid Area Calculation by Toby Jacobson (2)

Trapezoid Area Calculation by Toby Jacobson (2)
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2016-07-21 22:58
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the calculation of trapezoid area. Key mathematical concepts include the properties and area formula of a trapezoid. Using GeoGebra commands such as Line, 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. Line(A, B) → f
  2. Line(C, f) → g
  3. Point(g) → D
  4. Point(g) → E
  5. Point(f) → F
  6. Point(f) → G
  7. Segment(F, D) → h
  8. Segment(G, E) → i
  9. OrthogonalLine(C, g) → j
  10. Intersect(f, j) → H
  11. Segment(C, H) → height
  12. Midpoint(h) → I
  13. Midpoint(i) → J
  14. Polygon(F, I, J, G) → poly1, f_1, i_1, j_1, g_1
  15. Polygon(I, D, E, J) → poly2, i_2, d, e, j_2
  16. Rotate(I, (-α), J) → I'
  17. Rotate(D, (-α), J) → D'
  18. Rotate(E, (-α), J) → E'
  19. Rotate(J, (-α), J) → J'
  20. Polygon(I', D', E', J') → poly2', i', d', e', j'
  21. Segment(D, E) → l
  22. Segment(E', D') → base1
  23. Segment(F, G) → base2

AI Drawing Prompt Reference

Draw a trapezoid with a bottom base and a parallel top base. Place two points on the top base as its endpoints, and two points on the bottom base as its endpoints. Connect the left top endpoint to the left bottom endpoint to form the left leg, and the right top endpoint to the right bottom endpoint to form the right leg. From one top endpoint, drop a perpendicular to the bottom base, marking the foot as the height. Take the midpoints of both legschers, then connect these midpoints with the bottom endpoints to form two triangular regions. Rotate the top base segment around the right leg midpoint by a certain angle, obtaining new top endpoints, and connect them to form the new top base. Finally, label the lengths of the top base, bottom base, and height.
The prompt above was compiled from the original drawing commands and is for reference only.