Chapter 8.4, Problem 18PPE

To determine

To find an expression for the area of shaded region from given figure

  

Answer to Problem 18PPE

The area of shaded region is $6x+9$ .

Explanation of Solution

Given information:

Given square

  

Since inner square has a side of length $x\text{units}\text{.}$

  $\Rightarrow \text{area}\text{of}\text{inner}\text{square}=x^2\mathrm{.......}(i)$

And area of outer square has side of length $x+3\text{units}\text{.}$

  $\Rightarrow \text{area}\text{of}\text{outer}\text{square}={\left(x+3\right)}^2\mathrm{.......}(ii)$

Thus, the area of shaded region is ${\left(x+3\right)}^2-x^2$

  $\begin{array}{l}=x^2+6x+9-x^2\\ =6x+9\end{array}$

Hence, the area of shaded region is $6x+9$ .