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Area of a Parallelogram by GeoGebra Materials Team

Area of a Parallelogram by GeoGebra Materials Team
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2012-02-22 19:40
PolygonGeometric Construction
In collections Area, Surface Area, Volume--Nets Area, perimeter and volume of shapes Area, Perimeter and Volume of shapes
This example demonstrates how to calculate the area of a parallelogram using geometric construction. Key mathematical concepts include the properties and area formula of a parallelogram. GeoGebra commands used include Segment, OrthogonalLine, Point, Intersect, etc. Suitable for middle school and above students to learn geometric construction and area calculation.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a''
  2. OrthogonalLine(B, a'') → b_2
  3. OrthogonalLine(A, a'') → c
  4. Point(c) → C
  5. OrthogonalLine(C, c) → d
  6. Intersect(b_2, d) → D
  7. Segment(A, C) → e
  8. Point(Circle[E, a'']) → F
  9. Segment(E, F) → f
  10. OrthogonalLine(E, f) → g
  11. Point(Circle[E, e]) → G
  12. Segment(E, G) → h_1
  13. Circle(E, G) → k
  14. Intersect(k, g, 1) → H
  15. OrthogonalLine(H, g) → i
  16. OrthogonalLine(F, f) → j_2
  17. Intersect(i, j_2) → I
  18. Line(E, F) → n
  19. Segment(H, I) → j
  20. Point(j) → J
  21. OrthogonalLine(J, n) → l
  22. Intersect(j_2, n) → K
  23. Intersect(l, n) → M
  24. Segment(J, M) → h'
  25. Point(a'') → L
  26. OrthogonalLine(L, a'') → a
  27. Intersect(d, a) → N
  28. Polygon(A, L, N, C) → P, b, l_1, n_1, h
  29. Circle(J, b) → p
  30. Intersect(d, i) → O
  31. Intersect(p, i, 1) → Q
  32. Circle(E, b) → q
  33. Intersect(q, n, 1) → R
  34. Polygon(E, J, Q, R) → S, e_1, j_1, q_1, b'
  35. Segment(M, R) → m

AI Drawing Prompt Reference

Draw a parallelogram and construct its area using auxiliary lines and points. Start by creating two parallel lines a and a''. On a'', take point B and draw a perpendicular line b_2 from B to a. On a, take point A and draw a perpendicular line c from A to a. The intersection of c and b_2, point C, is one vertex of the parallelogram. Next, draw a perpendicular line d from C to c, and the intersection of d and b_2, point D, is another vertex of the parallelogram. Connect AD, and draw a circle with center E passing through A, intersecting c at point F, which is another vertex of the parallelogram. Draw a perpendicular line g from E to EF, and the intersection of g and c, point G, is another vertex of the parallelogram. Connect EG to construct the area of the parallelogram.
The prompt above was compiled from the original drawing commands and is for reference only.