# USE MODELS TO FIND AREAS OF COMPOUND FIGURES

## About "Use models to find areas of compound figures"

Use models to find areas of compound figures :

Area is measured in square units. We can use squares as models to find the area of rectangles and squares. We can also find the area of some composite figures using squares.

## Use models to find areas of compound figures - Examples

Example 1 :

Find the area of the shaded region.

Solution :

One way :

Count the square units. The figure shows that there are 48 square units.

Another Way :

Step 1 :

Decompose the figure into rectangles and squares.

The figure can be broken into two rectangles and one square as given below.

Step 2 :

Find the area of the parts. Then add them together.

Area of rectangle 1 :  3 × 5 = 15

Area of square  :  3 × 3 = 9

Area of rectangle 2 :  4 × 6 = 24

Area of the given composite figure is

=  15 + 24 + 9

=  48 square units.

Example 2 :

Find the area of the shaded region.

Solution :

Step 1 :

Decompose the figure into parts.

The figure can be broken into one rectangle and one square as given below.

Step 2 :

Find the area of the parts. Then add them together.

Area of rectangle  :  2 × 4 = 8

Area of square  :  3 × 3 = 9

Area of the given composite figure is

=  8 + 9

=  17 square units.

Example 3 :

Find the area of the shaded region.

Solution :

Step 1 :

Decompose the figure into parts.

The figure can be broken into two rectangles as given below.

Step 2 :

Find the area of the parts. Then add them together.

Area of rectangle 1  :  9 × 2 = 18

Area of rectangle 2  :  4 × 7 = 28

Area of the given composite figure is

=  18 + 28

=  46 square units.

Example 4 :

Find the area of the shaded region.

Solution :

Step 1 :

Decompose the figure into parts.

The figure can be broken into four rectangles and one square as given below.

Step 2 :

Find the area of the parts. Then add them together.

Area of rectangle 1  :  3 × 2 = 6

Area of rectangle 2  :  2 × 3 = 6

Area of square  :  4 × 4 = 16

Area of rectangle 3  :  1 × 2 = 2

Area of rectangle 4  :  1 × 2 = 2

Area of the given composite figure is

=  6 + 6 + 16 + 2 + 2

=  32 square units.

Example 5 :

Find the area of the shaded region.

Solution :

Count the square units inside the shaded region. The figure shows that there are 32 square units.

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