Chapter 6.1, Problem 44E

To determine

To calculate : the ratio of the area of the shaded region to the area of the unshaded region.

Answer to Problem 44E

The ratio of the area of the shaded region to the area of the unshaded region is $1:3$ .

Explanation of Solution

Given information :

Length of each side of square is given as $2s$ .

The shaded region is a square having each side equal to $s$ .

Formula used :

Formula used for area of square,

  $\text{Area}={\left(\text{side}\right)}^2$

Calculation :

The ratio of the area of the shaded region to the area of the unshaded region can be derived as,

Area of unshaded region = area of square − area of shaded region.

The area of square,

  $\begin{array}{l}\text{Area}={\left(\text{side}\right)}^2\\ \text{Area}={\left(2s\right)}^2\\ \text{Area}=4s^2\end{array}$

The area of the shaded region,

  $\begin{array}{l}\text{Area}={\left(\text{side}\right)}^2\\ \text{Area}={\left(s\right)}^2\\ \text{Area}=s^2\end{array}$

Area of unshaded region = area of square − area of shaded region

Area of unshaded region = $4s^2-1s^2$

Area of unshaded region = $3s^2$

The ratio of the area of the shaded region to the area of the unshaded region can be derived as,

The ratio of area of shaded region : ratio of area of unshaded region

  $\begin{array}{l}=s^2:3s^2\\ =1:3\end{array}$

Therefore,

The ratio of the area of the shaded region to the area of the unshaded region is $1:3$ .