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Area of Obtuse Triangle

Area of Obtuse Triangle
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2012-04-05 16:33
TriangleTrigonometryGeometric Construction
This example demonstrates how to calculate the area of an obtuse triangle, highlighting that the perpendicular height may lie outside the triangle itself. Key math concepts include triangle area formulas, obtuse angle properties, and height definitions. GeoGebra commands like Point, Segment, Rotate, Angle, OrthogonalLine, Line, Circle, Intersect, Distance, Midpoint, Polygon, Dilate, Vector, and Translate are used to construct the figure and compute the area. Suitable for high school mathematics education, illustrating area calculation methods and height positioning in obtuse triangles.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → c
  3. Rotate(B, α, A) → B'_1
  4. Angle(B, A, B'_1) → β
  5. OrthogonalLine(A, c) → d
  6. Line(A, B'_1) → g
  7. Line(A, B) → e
  8. Point(e) → C
  9. Circle(C, b) → f
  10. Intersect(f, g) → D, E
  11. Segment(E, B) → h
  12. Distance(E, C) → distanceEC
  13. Distance(A, B) → distanceAB
  14. OrthogonalLine(E, d) → i
  15. OrthogonalLine(B, e) → k
  16. Intersect(i, k) → F
  17. Intersect(i, d) → G
  18. Midpoint(G, F) → H
  19. Midpoint(A, B) → I
  20. Polygon(A, I, H, G) → poly1, a_1, i_1, h_1, g_1
  21. Distance(G, H) → distanceGH
  22. Distance(G, A) → distanceGA
  23. OrthogonalLine(E, e) → l
  24. Intersect(l, e) → J
  25. Distance(J, E) → distanceJE
  26. Midpoint(E, A) → K
  27. Line(K, e) → m
  28. Intersect(m, d) → L
  29. Intersect(h, m) → M
  30. Polygon(A, B, M, L) → poly2, a_2, b_1, m_1, l_1
  31. Polygon(A, L, K) → poly3, k_1, a_3, l_2
  32. Polygon(E, K, M) → poly4, m_2, e_1, k_2
  33. Rotate(M, γ, M) → M'_1
  34. Rotate(E, -γ, M'_1) → E'
  35. Rotate(K, -γ, M'_1) → K'_1
  36. Rotate(M, -γ, M'_1) → M'
  37. Polygon(E', K'_1, M') → poly4', m'_1, e'_1, k'_1
  38. Dilate(B, j, A) → B'
  39. Vector(A, B') → u
  40. Translate(A, u) → A'
  41. Translate(L, u) → L'
  42. Translate(K, u) → K'
  43. Polygon(A', L', K') → poly3', k', a', l'
  44. Distance(A, L) → distanceAL