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Area of Parallelograms and Triangles

Area of Parallelograms and Triangles
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2017-11-15 07:24
TrianglePolygonVectorGeometric Construction
This example demonstrates the calculation methods for the areas of parallelograms and triangles. It involves core mathematical concepts such as area formulas, vector operations, and geometric transformations. Key GeoGebra commands used in the construction include Polygon, Rotate, Vector, Translate, Angle, OrthogonalLine, Intersect, and Segment. It is suitable for high school mathematics instruction to help students visually understand the principles of area calculation.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Polygon(B, D, C) → t2, c_1, b_1, d
  3. Rotate(B, 45°, D) → B'
  4. Rotate(D, 45°, D) → D'
  5. Rotate(C, 45°, D) → C'
  6. Polygon(B', D', C') → t2', c', b', d'
  7. Vector(B', E) → u
  8. Translate(B', u) → B''
  9. Translate(D', u) → D''
  10. Translate(C', u) → C''
  11. Polygon(B'', D'', C'') → t2'', c'', b'', d''
  12. Rotate(A, (-(135°)), B) → A'
  13. Rotate(B, (-(135°)), B) → B'_1
  14. Rotate(C, (-(135°)), B) → C'_1
  15. Polygon(A', B'_1, C'_1) → t1', c'_1, a', b'_1
  16. Vector(C'_1, F) → v
  17. Translate(A', v) → A''
  18. Translate(B'_1, v) → G
  19. Translate(C'_1, v) → H
  20. Polygon(A'', G, H) → t1'', h, a'', g
  21. Angle(A, C, D) → α
  22. Angle(C, D, B) → β
  23. Angle(D, B, A) → γ
  24. Angle(B, A, C) → δ
  25. Angle(t2'') → ε, ζ, η
  26. Angle(t1'') → θ, ι, κ
  27. OrthogonalLine(D'', d'') → f
  28. OrthogonalLine(A'', a'') → i
  29. Intersect(f, d'') → I
  30. Intersect(i, a'') → J
  31. Segment(D'', I) → j
  32. Segment(A'', J) → k