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Q44.

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Found in: Page 280

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Find the ratio of the area of the shaded region to the area of the unshaded region. The figures are composed of squares and triangles.

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

See the step by step solution

## Step 1 . Given

Given that the length of each side of the square = 2s.

The shaded region is a square with each side = s.

## Step 2 . To determine

We have to find the ratio of the area of the shaded region to the area of the unshaded region.

## Step 3 . Calculation

We will use this concept:

Area of the unshaded region = area of the square – area of the shaded region.

The area of the big square is given by:

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

The area of the shaded region or the area of the smaller square is given by:

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

Hence,

= area of the square – area of the shaded region.

= $4{s}^{2}-1{s}^{2}$

=$3{s}^{2}$

So, the ratio of the area of the shaded region to the area of the unshaded region is given as,

The area of the shaded region: the area of the unshaded region

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

Hence, the ratio of the area of the shaded region to the area of the unshaded region is 1:3.