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Polygon Area Summary

Polygon Area Summary
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2014-02-18 22:34
PolygonCoordinate Geometry
This example demonstrates how to calculate the area of a polygon using geometric construction. Key mathematical concepts include polygons, random variables, and arithmetic operations. Using GeoGebra commands such as Polygon, Line, Intersect, etc., the construction of polygons and their area calculation are illustrated. Suitable for middle school and above students to learn polygon area calculation methods.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Line(A, B) → trLine1
  3. Line(C, A) → trLine2
  4. OrthogonalLine(C, trLine1) → d
  5. Intersect(trLine1, d) → TrH1
  6. Segment(C, TrH1) → trH1
  7. OrthogonalLine(B, trLine2) → f
  8. Intersect(trLine2, f) → TrH2
  9. Segment(B, TrH2) → trH2
  10. Segment(B, TrH1) → trBseg1
  11. Segment(A, TrH1) → trBseg2
  12. Segment(C, TrH2) → trBseg3
  13. Segment(A, TrH2) → trBseg4
  14. Text("h", Midpoint[trH1]) → trHText1
  15. Text("h", Midpoint[trH2]) → trHText2
  16. Text("b", Midpoint[c]) → trBText1
  17. Text("b", Midpoint[b]) → trBText2
  18. Line(D, E) → pLine
  19. Line(F, E) → pLine2_1
  20. Line(F, pLine) → pLine2
  21. Line(D, pLine2_1) → pLine3
  22. Intersect(pLine2, pLine3) → G
  23. Polygon(D, E, F, G) → poly2, d_1, e_1, f_1, g
  24. OrthogonalLine(F, pLine) → h
  25. Intersect(pLine, h) → PH1
  26. Segment(F, PH1) → pH1
  27. Segment(E, PH1) → pBseg1
  28. Segment(D, PH1) → pBseg2
  29. OrthogonalLine(F, pLine3) → i
  30. Intersect(pLine3, i) → PH2
  31. Segment(PH2, F) → pH2
  32. Segment(PH2, G) → pBseg3
  33. Segment(D, PH2) → pBseg4
  34. Text("h", Midpoint[pH1]) → pHText1
  35. Text("b", Midpoint[D, E]) → pBText1
  36. Text("h", Midpoint[pH2]) → pHText2
  37. Line(H, I) → tLine1
  38. Ray(J, J + Vector[I, H]) → tRay
  39. Point(tRay) → K
  40. Polygon(H, I, J, K) → poly3, h_1, i_1, j, k
  41. OrthogonalLine(J, tLine1) → l
  42. Intersect(l, tLine1) → TH
  43. Segment(J, TH) → th
  44. Text("h", Midpoint[th]) → tHText
  45. Text("a", Midpoint[H, I]) → tAText
  46. Text("b", Midpoint[K, J]) → tBText
  47. Segment(TH, I) → tBseg1
  48. Segment(H, TH) → tBseg2
  49. Text("b", Midpoint[E, F]) → pBText2

AI Drawing Prompt Reference

Draw three polygons to illustrate area formulas. First, a triangle with three sides, drop perpendiculars from vertices to opposite sides, mark the feet, draw segments for heights, label the midpoint of each height with 'h' and the midpoint of each base with 'b'. Second, a parallelogram formed by two pairs of parallel lines, drop a perpendicular from a vertex to the base, mark the foot, draw a segment for the height, label 'h' and 'b' similarly. Third, a trapezoid with one base, one slanted side, and two parallel lines, drop a perpendicular from a vertex to the base, mark the foot, draw a segment for the height, label 'a' at the midpoint of the base, 'b' at the midpoint of the slanted side, and 'h' on the height. Use solid lines and clear labels.
The prompt above was compiled from the original drawing commands and is for reference only.