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Area from cross product (diagonal vectors)

Area from cross product (diagonal vectors)
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2020-01-25 20:52
PolygonVectorGeometric Construction
This example demonstrates how to calculate the area of a parallelogram using the cross product of vectors, involving core math concepts like vectors, cross product, and geometry. Construction highlights the use of GeoGebra commands/objects such as Intersect, Vector, Translate, Polygon, and PointIn. Suitable for high school and above students to learn vector applications in geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → u
  3. Vector(A, C) → v
  4. Translate(D, v) → D'
  5. Vector(D, D') → w
  6. Translate(E, u) → E'
  7. Vector(E, E') → a
  8. Polygon(D, E, D', E') → q1, d, e, d', e'
  9. PointIn(q1) → Pointq1
  10. Polygon(A, C, B) → t1, b, a_1, c
  11. PointIn(t1) → Pointt1
  12. Intersect(e, e') → F
  13. Polygon(F, E, D) → t3, d_1, f_2, e_1
  14. PointIn(t3) → Pointt3
  15. Polygon(F, E', D') → t2, f, f_1, g
  16. PointIn(t2) → Pointt2
  17. Polygon(D, E, D', E') → q2, d_2, e_2, h, i