Lesson 16 — Activity 2:

Measuring the Perimeter of Irregular Shapes

In the last lesson, you learned how to find the perimeter (or distance around an object) that was a regular shape. However, in real life, figures are often irregular.

Irregular shapes have sides of any length. To find the perimeter of an irregular shape, you just count the lengths around the entire object. It doesn't matter if the lengths are different.

For example, say you wanted to find the perimeter of this skating rink. You know that to find perimeter, you just need to add up all the sides.

P = 7 cm + 2 cm + 2 cm + 2 cm + 7 cm + 2 cm + 2 cm + 2 cm = 26 cm

Sometimes you will need to find the perimeter of an irregular shape when one (or more) of the measurements of the sides are missing.

Here is an irregular shape with the measurement of two sides missing.

To find its perimeter, you must first find the missing measurements. Imagine that the shape is divided into rectangles. What is the length of each segment?

You know that the top of the shape is 5 in, and the bottom section of the shape is 3 in, therefore, you can subtract to find out the length of the missing side.

5 in – 3 in = 2 in

The measurement of the missing side is 2 in.

You can do the same to find the second missing measurement. You know that the left side of the shape is 2 in, and the right section of the shape is 1 in. Therefore, you can subtract again to find out the length of the missing side.

2 in - 1 in = 1 in

Now you can add up all the sides to find the perimeter of the shape.

5 + 1 + 2 + 1 + 3 + 2 = 14

P = 14 in

Let's try another one!

Look at the shape to the right. More than one of the sides are missing.

First, you need to find the length of the missing sides, and then you can add up all the sides to find the perimeter!

First, you can find the missing length of the bottom side of the shape by subtracting:

6 cm – 2 cm = 4 cm

The length of the bottom of the shape is 4 cm.

Next, you need to ADD to find the length of the missing side on the left side of the shape.

4 cm + 3 cm = 7 cm

If the right side of the shape is equal to 7 cm, then the length of the left side of the shape is also 7 cm.

Finally, you can add up all the sides to find the perimeter of the irregular shape.

6 cm + 4 cm + 2 cm + 3 cm + 4 cm + 7 cm = 26 cm

The perimeter of this shape is 26 cm.

  Self-check!