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Area of Triangle by Malin Christersson

Area of Triangle by Malin Christersson
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2014-02-18 22:23
TriangleCoordinate GeometryGeometric Construction
In collections Area of a triangle and Circle KS3 Theta2 U2 Area and volume
This example demonstrates how to calculate the area of a triangle using geometric construction. Key mathematical concepts include the area formula for triangles and coordinate geometry. It utilizes commands such as Line, Polygon, Segment, Angle, and Midpoint in GeoGebra. Suitable for middle school and above students learning geometry and area calculation.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → C
  4. Polygon(A, B, C) → poly1, c, a_1, b_1
  5. OrthogonalLine(C, a_1) → d
  6. OrthogonalLine(A, c) → e
  7. Intersect(d, e) → D
  8. Polygon(A, B, C, D) → poly2, a_2, b_2, c_1, d_1
  9. Line(E, F) → f
  10. OrthogonalLine(F, f) → g
  11. Point(g) → G
  12. OrthogonalLine(G, g) → h
  13. OrthogonalLine(E, f) → i
  14. Intersect(h, i) → H
  15. Polygon(E, F, G, H) → poly3, e_1, f_1, g_1, h_1
  16. Point(g_1) → I
  17. Polygon(E, F, I) → poly4, i_1, e_2, f_2
  18. OrthogonalLine(I, e_1) → p
  19. Intersect(p, e_1) → N
  20. Segment(I, N) → hSeg
  21. Polygon(J, K, L) → poly5, l, j, k
  22. Line(J, j) → m
  23. Line(L, l) → n
  24. Intersect(m, n) → M
  25. Polygon(J, K, L, M) → poly6, j_1, k_1, l_1, m_1
  26. Angle(C, B, A) → β
  27. Midpoint(hSeg) → mid
  28. Text("h", mid + (0.1, 0)) → hText
  29. Midpoint(E, F) → mid2
  30. Text("b", mid2 + ((-0.05), (-0.12))) → bText

AI Drawing Prompt Reference

Draw a triangle ABC, then draw a perpendicular line from point C to AB, intersecting at point D, forming quadrilateral ABCD. Next, draw a perpendicular line from point D to AB, intersecting at point E, forming quadrilateral ABDE. Continue by drawing a perpendicular line from point E to AB, intersecting at point F, forming quadrilateral ABEF. Then, draw a perpendicular line from point F to AB, intersecting at point G, forming quadrilateral ABFG. Next, draw a perpendicular line from point G to AB, intersecting at point H, forming quadrilateral ABGH. Continue by drawing a perpendicular line from point H to AB, intersecting at point I, forming quadrilateral ABHI. Then, draw a perpendicular line from point I to AB, intersecting at point J, forming quadrilateral ABIJ. Finally, calculate the area of triangle ABC.
The prompt above was compiled from the original drawing commands and is for reference only.