MathPlotAI Logo MathPlotAI

Maximum Area with Fixed Angle

Maximum Area with Fixed Angle
Loading the math board and drawing, please wait…
2018-04-07 23:32
AngleTrigonometryOptimization
This example explores the optimization of a quadrilateral's area. Given a perimeter and a fixed 30-degree angle, how can we construct a quadrilateral with the maximum area? By adjusting the side lengths and angles, observe the changes in the quadrilateral's area. This example involves trigonometry, quadrilaterals, and optimization problems. It uses commands such as Ray, Point, Ellipse, Angle, and Polygon in GeoGebra, suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Ray(A, A + (cos(π / 6), sin(π / 6))) → f'
  2. Point(f') → D
  3. Ray(A, A + (1, 0)) → f
  4. Point(f) → B
  5. Ellipse(D, B, C_1) → c
  6. Point(c) → C
  7. Angle(B, A, D) → α
  8. Polygon(A, B, C, D) → q1, a_1, b_1, c_1, d
  9. Perimeter(q1) → e
  10. Angle(C, B, A) → β
  11. Angle(D, C, B) → γ
  12. Angle(A, D, C) → δ
  13. Textfield(ad) → InputBox1
  14. Textfield(ab) → InputBox2