Chapter 11.2, Problem 4CCYP

To determine

To find: The area of the kite.

Answer to Problem 4CCYP

The area of the kite is $168{\text{in}}^2$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the formula for the area of the kite is,

  $A=\frac{1}{2}{d}_1{d}_2$

Consider the calculation for half of the diagonal is,

  $\begin{array}{l}{10}^2=6^2+{\left(\frac{d_1}{2}\right)}^2\\ {\left(\frac{d_1}{2}\right)}^2=64\\ \frac{d_1}{2}=8\\ d_1=16\end{array}$

Consider the measurement for the other diagonal is,

  $\begin{array}{l}{17}^2={\left(8\right)}^2+{\left(d_2\right)}^2\\ {\left(d_2\right)}^2=225\\ d_2=15\end{array}$

Then,

  $\begin{array}{c}{d}_2=15+6\\ =21\text{in}\end{array}$

Thus, the area of the kite is,

  $\begin{array}{c}A=\frac{\left(16\right)\left(21\right)}{2}\\ =168{\text{in}}^2\end{array}$