USE MODELS TO FIND AREAS OF COMPOSITE SHAPES

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 shapes using squares.

Example 1 : 

Find the area of the shaded region.

Solution :

One way : 

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

Another Way :

Step 1 :

Decompose the shape into rectangles and squares.

The shape 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 shape is

=  15 + 24 + 9 

=  48 square units

Example 2 : 

Find the area of the shaded region.

Solution :

Step 1 :

Decompose the shape into parts.

The shape 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 shape is

=  8 + 9 

=  17 square units

Example 3 : 

Find the area of the shaded region.

Solution :

Step 1 :

Decompose the shape into parts.

The shape 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 shape is

=  18 + 28 

=  46 square units

Example 4 : 

Find the area of the shaded region.

Solution :

Step 1 :

Decompose the shape into parts.

The shape 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 shape 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 shape shows that there are 32 square units.

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