Chapter 11.4, Problem 3CYU

To determine

To calculate: The area of the square.

Answer to Problem 3CYU

The area of the square is $81{\text{ in}}^2$.

Explanation of Solution

Given information: The length of half of the diagonal of the square is $9\text{ in}$ .

Formula Used: The area of the square is,

  $A=S^2$ .......(1)

• Here, S is the length of the side of the square.

Calculation:

The length of the half of the diagonal of the square is $9\text{ in}$ .

Therefore, the length of the diagonal is,

  $\begin{array}{c}D=2\times 9\\ =18\text{ in}\end{array}$

The angle of the square is,

  $\begin{array}{c}\theta =\frac{{360}^{\circ }}{4}\\ ={90}^{\circ }\end{array}$

Consider the figure shown below:

  

The length of the side of the square is $9\text{ in}$ .

Substitute the values on equation (1).

  $\begin{array}{c}A=S^2\\ =9^2\\ =81\end{array}$

Hence, the area of the square is $81{\text{ in}}^2$.