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Area of a Triangle by David T

Area of a Triangle by David T
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2013-03-22 08:15
TriangleCoordinate GeometryGeometric Construction
In collections Unit 11: Extending Perimeter, Circumference, and Area 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 properties of triangles and coordinate geometry. Using GeoGebra commands such as Segment, LineBisector, and Polygon, one can construct a triangle and calculate its area. Suitable for middle school and above students learning geometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → AB
  2. LineBisector(AB) → b
  3. Point(b) → D
  4. Point(b) → C
  5. Segment(D, C) → CD
  6. OrthogonalLine(A, CD) → g
  7. Segment(C, A) → c
  8. Segment(D, A) → d
  9. Intersect(b, g) → E
  10. Polygon(C, E, A) → poly1, a_1, c_1, e_1
  11. Polygon(A, E, D) → poly3, d_4, a_2, e_3
  12. Midpoint(C, A) → F
  13. Midpoint(A, D) → H
  14. Rotate(A, rotateΔ, H) → A'
  15. Rotate(E, rotateΔ, H) → E'
  16. Rotate(D, rotateΔ, H) → D'
  17. Polygon(A', E', D') → poly3', d', a', e'
  18. Rotate(C, rotateΔ, F) → C'
  19. Rotate(E, rotateΔ, F) → E'_1
  20. Rotate(A, rotateΔ, F) → A'_1
  21. Polygon(C', E'_1, A'_1) → poly1', a'_1, c', e'_1
  22. Midpoint(A, E) → J
  23. Midpoint(D, C) → K
  24. Angle(C, E, A) → α
  25. Segment(A, E) → a
  26. Segment(C, E) → i
  27. Segment(D, E) → j
  28. Polygon(D, C, A) → poly5, a_3, d_5, c_3
  29. Midpoint(D, E) → G

AI Drawing Prompt Reference

Draw a triangle ABC, construct segments AB, CD, and AE, and use these to construct altitudes and medians. Then rotate to construct triangle A'E'D', and calculate and display the area of triangle ABC.
The prompt above was compiled from the original drawing commands and is for reference only.