Chapter 8.4, Problem 47PPS

To determine

To find: The area of the shaded region

Answer to Problem 47PPS

  $6x+3$

Explanation of Solution

Given:

  

Calculation:

The area of the inner square is given by

  $\begin{array}{l}{\left(x-1\right)}^2\\ =x^2-2x+1\end{array}$

And the area of outer square is given by

  $\begin{array}{l}{\left(x+2\right)}^2\\ =x^2+4x+4\end{array}$

Hence, the area of the shaded region is given by

  $\begin{array}{l}{x}^2+4x+4-\left(x^2-2x+1\right)\\ =x^2+4x+4-x^2+2x-1\\ =6x+3\end{array}$