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Parallelogram Area Demonstration by C.J. Carlson

Parallelogram Area Demonstration by C.J. Carlson
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2018-03-09 06:42
PolygonVectorGeometric Construction
This example demonstrates the calculation method for the area of a parallelogram. It involves core mathematical concepts such as properties of parallelograms, area formula of triangles, and vector operations. Key GeoGebra commands and objects used in the construction include Intersect (intersection), Point (point), CircleArc (arc), Segment (segment), Ray (ray), Line (line), OrthogonalLine (perpendicular line), Polygon (polygon), Distance (distance), Vector (vector), and Translate (translation). It is suitable for middle school students and above learning the area formula of parallelograms and vector applications.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A_1
  2. Point(yAxis) → B_1
  3. Point(xAxis) → C_1
  4. CircleArc(A_1, C_1, B_1) → c
  5. Point(c) → A
  6. Segment(A_1, A) → a
  7. Ray(A_1, C_1) → b
  8. Point(b) → B
  9. Line(B, a) → d
  10. Line(A, b) → e
  11. Intersect(e, d) → C
  12. OrthogonalLine(A, b) → f
  13. OrthogonalLine(C, b) → g
  14. Intersect(f, b) → G
  15. Intersect(g, b) → H
  16. Polygon(A, G, A_1) → poly1, a_1, d_1, g_1
  17. Polygon(A, G, B, C) → poly2, d_2, g_2, e_1, f_1
  18. Distance(G, H) → distanceGH
  19. Point(Circle[I, distanceGH]) → J
  20. Segment(I, J) → h
  21. Point(h) → K
  22. Vector(I, K) → u
  23. Translate(A, u) → D'
  24. Translate(G, u) → G'
  25. Translate(A_1, u) → A'
  26. Polygon(D', G', A') → poly1', a', d', g'