Finding the perimeter and area of composite shapes (otherwise known as irregular figures) is fairly simple, but it does take a little extra thought. Composite shapes are made by combining two or more smaller shapes into one larger figure. The figure below is a composite shape, made by combining a square and a rectangle. If we add a dashed line into the middle of the figure, the square and rectangle become very clear.

To find the perimeter and area of different composite shapes, you’ll first want to divide the larger figure into its smaller shapes, like we did above. After that, you’ll assess the figure for any missing information and perform your calculations.

EXAMPLE: Find the perimeter and area of the shape below.

First, divide the larger figure into smaller shapes. (There are frequently multiple ways of doing this step, but for the case of our example we’ll divide it into one square and one rectangle.) Then, use the information you know to add in the missing side lengths.

PERIMETER:
Perimeter is always the path around the object. Now that you know all of the side lengths, just add them together to find the perimeter.

P = 10 in + 10 in + 5 in + 5 in + 5 in + 5 in
P = 40 in.

AREA:
Area is the space inside. To find the area of the composite shape, find the area of the square and the rectangle individually. Then, add them together.

Area of this composite shape = Area of the square + Area of the rectangle.
Area = 25 in² + 50 in²
Area = 75 in²