MathPlotAI Logo MathPlotAI

Animation to Show Triangle Area

Animation to Show Triangle Area
Loading the math board and drawing, please wait…
2017-02-26 06:29
TriangleVectorCoordinate Geometry
This example demonstrates the calculation of a triangle's area through animation. Key mathematical concepts include the area formula for triangles and vectors. GeoGebra commands used include Point, Semicircle, Polygon, Angle, Rotate, etc. Suitable for middle school and above students to learn geometric construction and area calculation.

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(B)], y(K)) → L
  7. Semicircle(C, B) → d
  8. Polygon(A, B, C) → poly1, c, a, b
  9. Intersect(f, b) → E
  10. Intersect(f, a) → D
  11. Intersect(f, g) → F
  12. Point(d, 1 - animate) → G
  13. Angle(G, D, C) → α
  14. Polygon(D, F, C) → poly2, c_1, d_1, f_1
  15. Rotate(D, (-α), D) → D'
  16. Rotate(F, (-α), D) → F'
  17. Rotate(L, (-α), D) → C'
  18. Polygon(D', F', C') → poly2', c', d', f'
  19. Polygon(F, C, E) → poly3, e, f_2, c_2
  20. Rotate(F, α, E) → F'_1
  21. Rotate(L, α, E) → C'_1
  22. Rotate(E, α, E) → E'
  23. Polygon(F'_1, C'_1, E') → poly3', e', f'_1, c'_1
  24. Segment(E, C) → h
  25. Segment(C, D) → i
  26. Polygon(I, E, D, H) → poly4, i_1, e_1, d_2, h_1
  27. Vector(H - (0, 1), I - (0, 1)) → u
  28. Vector(I - (0, 1), H - (0, 1)) → v
  29. Vector(J, M) → w
  30. Vector(M, J) → j
  31. Vector(N, J) → k
  32. Vector(J, N) → l
  33. LaTeX("\frac{h}{2}") → text3
  34. LaTeX("Area = \frac{bh}{2}") → text4