Kite Formula?

Question

Show how you can find an area formula for a kite using a reflection. (hint: Reflect half of the kite across its line of symmetry d sub 1 by folding the kite along d sub 1. How is the area of the triangle formed related to the area of the kite)

Answer 1

David,

 

If we fold the kite along the axis of symmetry, we get a triangle where the axis of symmetry forms the base and the folded axis (by definition perpendicular to the axis of symmetry) forms the altitude. The area of said triangle would be bh/2. Now since that triangle is exactly half of the kite, the area of the kite would be 2*bh/2 or just:

 

A = bh where b is d₁ and h is half of the secondary axis (d₂).

 

A_kite = d₁d₂ / 2

 

I hope that helps.