*Contributor: Rachel Lewis. Lesson ID: 12775*

In the area of geometry, can you find the area of simple figures? Are you on the perimeter when it comes to figuring the distance around figures? It's simple to find your way in and around composites!

categories

subject

Math

learning style

Visual

personality style

Beaver

Grade Level

Intermediate (3-5)

Lesson Type

Dig Deeper

Do you know what composes a composite figure? Can you find composite figures on the playground? Can you find their area and perimeter?

When you put a rectangle and a square together to make one shape, you create a *composite figure*.

A composite figure is a shape made up of two or more geometric figures.

Can you think of any real-world examples of a composite figure?

Sometimes, we need to find the area and perimeter of composite figures in real life, such as a swimming pool, a flower bed, or a house. Just as you can find the area and perimeter of a rectangle or a square, you can find the area and perimeter of a composite figure.

How do you find the area of a rectangle or square?

area = length *x* width

How do you think you would find the area of a composite figure?

To find the *area* of a composite figure, follow these three steps:

- Separate the composite figure into smaller, familiar figures. For example, if you have a composite figure made of a rectangle and a square, separate the figure into each shape.
- Find the area of each smaller figure. For example, find the area of the rectangle. Then, find the area of the square.
- Add the areas of each figure together to find the total area of the composite figure.

Can you use the three steps above to find the area of the composite figure below?

**Step 1**

- Separate the composite figures into smaller figures. You can separate the composite figure into rectangle A and rectangle B.

**Step 2**

- Find the area of each smaller figure.
- Let’s find the area of rectangle A: area of rectangle A = length x width, or area of rectangle A = 6 x 7, so area of rectangle A = 42 m
^{2}. - Now, let’s find the area of rectangle B:
- First, you need to find the length of side RS. RS = 5 + 6 + 5, or RS = 16 m.
- Area of rectangle B = length x width, or area of rectangle B = 16 x 4, so area of rectangle A = 64 m
^{2}.

**Step 3**

- Add the areas of each figure to find the total area of the composite figure:
- Area of rectangle A + area of rectangle B = area of the composite figure, or 42 m
^{2}+ 64 m^{2}= 106 m^{2}

Excellent!

What is the equation to find the *perimeter* of a rectangle or square?

- perimeter = sum of the lengths of all four sides, or
- perimeter = Side A + Side B + Side C + Side D

Can you think of a way to find the perimeter of a composite figure?

To find the perimeter of a composite figure, add all the distances around the closed figure. Find the sum of all the sides.

Look at the example below. Can you use the perimeter formula to find the perimeter of the composite figure?

To find the perimeter, you need to find the length of all the sides of the composite figure.

- First, let’s find the length of side AB:
- We know CD = 4 m, and EF = 6 m. So, we can add CD + EF to get the length of side AB.
- AB = 4 + 6 = 10 m.

- Next, find the length of side AC:
- We know BF = 10 m, and ED = 8 m. So, we can add BF + ED to get the length of side AC.
- AC = 10 + 8 = 18 m.

- Now you know the lengths of all the sides of the composite figures. Let’s find the sum of the lengths of all the sides to get our perimeter:
- Perimeter = AB + AC + BF + ED + CD + EF, or
- Perimeter = 10 + 18 + 10 + 8 + 4 + 6
- Perimeter = 56 m

Great work!

You may know how to find the area and perimeter of geometric shapes like rectangles and squares, but in real life there is a variety of shapes. If you know how to find the area and perimeter of composite shapes, you can find the area and perimeter of swimming pools, playgrounds, houses, and buildings.

In the *Got It? *section, you will complete an art project using your own composite figures.