Chapter 11.2, Problem 24PPS

To determine

To Prove: The formula for the area of $A=\frac{1}{2}{d}_1{d}_2$ .

Explanation of Solution

Given:

The given figure is shown in Figure 1

  

Figure 1

The values of $XZ=d_1$ and $WY=d_2$

Calculation:

From the figure the area of the kite is the sum of the area of the two triangle as,

  $\begin{array}{c}A=A_{WZY}+A_{WXY}\\ =\frac{1}{2}bh+\frac{1}{2}bh\\ =\frac{1}{2}\left(d_1\left(\frac{1}{2}{d}_2\right)\right)+\frac{1}{2}\left(d_1\left(\frac{1}{2}{d}_2\right)\right)\\ =\frac{1}{4}{d}_1{d}_2+\frac{1}{4}{d}_1{d}_2\end{array}$

Solve further as,

  $A=\frac{1}{2}{d}_1{d}_2$

Hence, proved.