MathPlotAI Logo MathPlotAI

Maximum Area of a Quadrilateral with Given Perimeter

Maximum Area of a Quadrilateral with Given Perimeter
Loading the math board and drawing, please wait…
2017-04-19 21:31
CirclePolygonTrigonometryOptimizationGeometric Construction
This example demonstrates how to construct a quadrilateral with maximum area given a fixed perimeter. It involves core concepts like perimeter, area, quadrilateral properties, incircle, and optimization. The construction uses commands such as Segment, Point, Circle, Intersect, Polygon, LineBisector, and Angle in GeoGebra. Suitable for high school mathematics education, helping students understand area optimization and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Point(f) → C
  3. Point(f) → D
  4. Point(f) → E
  5. Segment(A, C) → g
  6. Segment(C, D) → h
  7. Segment(D, E) → i
  8. Segment(E, B) → j
  9. Circle(F, g) → c
  10. Point(c) → G
  11. Circle(G, h) → d
  12. Point(d) → H
  13. Circle(H, i) → e
  14. Segment(F, G) → k
  15. Segment(G, H) → l
  16. Circle(F, j) → p
  17. Intersect(e, p) → I, J, ,
  18. Segment(H, J) → m
  19. Segment(J, F) → n
  20. Polygon(F, G, H, J) → poly1, f_1, g_1, h_1, j_1
  21. LineBisector(n) → q
  22. LineBisector(k) → r
  23. LineBisector(l) → s
  24. LineBisector(m) → t
  25. Intersect(q, r) → K
  26. Intersect(s, t) → L
  27. Circle(L, 0.02) → c_1
  28. Segment(L, G) → a
  29. Circle(L, a) → d_1
  30. Segment(L, F) → b
  31. Segment(L, J) → i_1
  32. Segment(L, H) → k_1
  33. Angle(H, G, F) → α
  34. Angle(F, J, H) → β