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Area of Parallelogram by h.hurchand

Area of Parallelogram by h.hurchand
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2015-03-20 10:48
VectorCoordinate GeometryGeometric Construction
In collections Deriving area formulas for Geometry
This example demonstrates how to calculate the area of a parallelogram using vector cross product. It involves core mathematical concepts like vectors, vector cross product, and geometric construction. The construction utilizes commands and objects such as Point, Segment, OrthogonalLine, Line, Intersect, Polygon, and Vector. It is suitable for high school mathematics teaching, helping students understand and apply vectors in geometric problems.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Segment(A, B) → a
  3. Point(a) → C
  4. OrthogonalLine(C, a) → b
  5. Point(b) → D
  6. Point(a) → E
  7. Segment(D, E) → c
  8. OrthogonalLine(D, b) → d
  9. Line(A, c) → e
  10. Intersect(d, e) → F
  11. OrthogonalLine(F, a) → f
  12. Intersect(f, a) → G
  13. Polygon(H_1, H_3, H_2) → poly1, h_2, h_1, h_3
  14. Polygon(A, F, D, E) → poly2, a_1, f_1, d_1, e_1
  15. Polygon(G, F, D, E) → poly3, g_1, f_2, d_2, e_2
  16. Vector(H, I) → u
  17. Vector(J, K) → v

AI Drawing Prompt Reference

Draw a parallelogram to calculate its area using vector cross product. Start by drawing a line segment, then take a point on it, and draw a perpendicular line through this point. Find the intersection of this perpendicular line with another line parallel to the original segment. Construct the parallelogram using these points and segments, labeling the base and height, and represent the base and height as vectors to demonstrate the geometric meaning of the vector cross product.
The prompt above was compiled from the original drawing commands and is for reference only.