MathPlotAI Logo MathPlotAI

Demonstrating the Area Formula for a Rhombus

Demonstrating the Area Formula for a Rhombus
Loading the math board and drawing, please wait…
2015-12-03 00:34
PolygonMatrix
In collections Area Formulas
This example illustrates one reason why the area formula A= rac{1}{2} d_1 d_2 works for rhombuses. It involves key math concepts like diagonals, symmetry, medians, perpendicular lines, and matrix transformations. The construction uses commands such as Segment, LineBisector, Intersect, Point, Circle, Polygon, Vector, Translate, Line, OrthogonalLine, Mirror. Suitable for high school students learning geometry to understand the geometric basis of the formula.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. LineBisector(a) → b
  3. Intersect(b, a) → C
  4. Point(b) → D
  5. Circle(C, D) → c
  6. Intersect(c, b, 2) → E
  7. Polygon(A, C, E) → poly2, e_1, a_2, c_1
  8. Polygon(C, B, E) → poly3, e_2, c_2, b_2
  9. Polygon(D, A, B) → poly1, b_1, d, a_1
  10. Vector(A, (r * x(D), r * y(D))) → u
  11. Translate(A, u) → A'
  12. Translate(C, u) → C'_1
  13. Translate(E, u) → E'_1
  14. Polygon(A', C'_1, E'_1) → poly2', e', a', c'
  15. Line(D, B) → e
  16. Translate(B, u) → B'_1
  17. Vector(B, B'_1) → v
  18. OrthogonalLine(B, d) → f
  19. Mirror(B'_1, f) → B''
  20. Vector(B, B'') → w
  21. Translate(C, w) → C'
  22. Translate(B, w) → B'
  23. Translate(E, w) → E'
  24. Polygon(C', B', E') → poly3', e'_1, c'_1, b'
  25. Segment(D, C) → g
  26. OrthogonalLine(F, b') → h
  27. Circle(F, 0.1 * b') → k
  28. Intersect(k, h) → G, H
  29. Line(H, b') → i
  30. Circle(H, 0.5 * b') → p
  31. Intersect(p, i) → I, J
  32. Vector(H, J) → z
  33. Vector(H, I) → j
  34. Circle(D, 0.1 * b') → q
  35. Intersect(q, b) → K, L
  36. Line(L, e') → l
  37. Circle(L, e') → s
  38. Intersect(s, l) → M, N
  39. Vector(L, M) → m
  40. Vector(L, N) → n