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Animation to Show the Area of a Parallelogram

Animation to Show the Area of a Parallelogram
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2017-06-26 17:03
PolygonVectorTransformationGeometric ConstructionSlider Animation
① This example uses an animated visual to demonstrate that the area of a parallelogram equals base times height, by cutting and translating a part to form an equivalent rectangle. ② Core mathematical concepts include the parallelogram area formula, geometric transformation (translation), and the principle of area conservation. ③ Construction details: GeoGebra commands such as Point, Polygon, Vector, Translate, DynamicCoordinates, and Semicircle are used to build the parallelogram, its translated copy, and auxiliary height lines; sliders drive the animation, and text objects display the area calculation. ④ Suitable for middle school geometry lessons, helping students grasp the derivation of the area formula, and useful for classroom demonstrations or self-paced exploration.

GeoGebra Commands & Parameters

  1. Point(xAxis) → H
  2. Point(xAxis) → I
  3. Sort({H, I}) → list1
  4. Element(list1, 1) → A
  5. Element(list1, 2) → B
  6. DynamicCoordinates(K, Min[Max[x(K), x(A)], (x(A) + x(B)) / 2], y(K)) → L
  7. Semicircle(C, B) → d
  8. Point(d, 1 - animate) → G
  9. Vector(H - (0, 1), I - (0, 1)) → u
  10. Vector(I - (0, 1), H - (0, 1)) → v
  11. Vector(J, M) → w
  12. Vector(M, J) → j
  13. Vector(N, J) → k
  14. Vector(J, N) → l
  15. Polygon(H, E, D) → poly1, d_1, h, e
  16. Translate(H, Vector[(animate * Vector[H, I])]) → H'
  17. Translate(E, Vector[(animate * Vector[H, I])]) → E'
  18. Translate(D, Vector[(animate * Vector[H, I])]) → D'
  19. Polygon(H', E', D') → poly1', d', h', e'
  20. Polygon(I, L, (x(I), y(L))) → poly2, f, i, l_1
  21. Polygon(H, I, L, (x(H), y(L))) → poly3, h_1, i_1, l_2, m
  22. Polygon(D, H, (x(H), y(D))) → poly4, n, d_2, h_2