Chapter 11.4, Problem 12PSC

To determine

Toprove : The area of kite = $\frac{1}{2}xy$ , if it is not convex.

Explanation of Solution

Given information :

Figure given of kite

Formula used :

Area of kite is = $\frac{1}{2}\times \left(\text{product of diagonals}\right)$

Proof :

If PQRS is a kite then its diagonals will be PR and QS

Since, it is given that figure is of kite and not convex

Thus,

Area of PQRS = $\frac{1}{2}\times \left(\text{product of diagonals}\right)$

= $\frac{1}{2}\times PR\times QS=\frac{1}{2}\left(xy\right)$

Hence proved