Area and Perimeter: Practice Finding a Missing Side Educational Resources K12 Learning, Geometry, Pre-Algebra, Math Lesson Plans, Activities, Experiments, Homeschool Help

Lesson Plan - Get It!

Audio:

Your soccer team is getting ready to practice, but the field you always use is flooded!

Before the rest of the team arrives for practice, you want to mark a new field across the street. You have spray paint, but you don't know all the measurements of the field.

All you know is that the boundary going around a soccer field is 220 yards. You think one side is 70 yards. You need to find the remaining missing sides in order to mark the field for practice!

Your team needs a new practice field ASAP!

Could you figure out the dimensions of the field?
Do you know what math would be involved to figure out something like this?

By now, you have learned how to find the perimeter and area of most shapes, especially quadrilaterals like squares and rectangles.

This information will help you solve the problem and save soccer practice!

If you need to review area and perimeter, visit Related Lessons in the right-hand sidebar.

First, let's sketch a soccer field and label the sides and information we already know:

soccer field

We know one side of the field is 70 yards. Since a soccer field is a rectangle, we also know the opposite side is 70 yards.

The other important information is that the measurement around the outside of the field is 220 yards.

What is this measurement?

Now, we know the formula to use! We will plug all the information we have into the formula for the perimeter of a rectangle.

Perimeter of Rectangle = 2 (Length) + 2 (Width)

Look at our drawing.

What do we know?

The perimeter is 220 yards and the length is 70 yards. Here is what the formula looks like now with that information:

220 = 2(70) + 2(W)

Now, we have a two-step equation to solve!

First, simplify what we have:

220 = 140 + 2(W)

Next, we need to get W alone, so we will first subtract 140 from both sides of the equal sign:

220 - 140 = 140 + 2(W) - 140

80 = 2 (W)

Last, we will divide both sides by 2 to solve for W:

80 ÷ 2 = 2 (W) ÷ 2

40 = W

Now, we know the missing sides! 40 yards!

soccer field

Let's quickly check our work!

Another way to find the perimeter of any shape is to simply add all the sides together:

70 + 70 + 40 + 40 = 220 yards

We get the same answer!

Is there another way you could have found the missing side?
Do you have any other strategies?

You could also start with the known perimeter (220) and subtract the sides you know:

220 - 70 - 70 = 80

80 represents the other two sides, which are equal:

80 ÷ 2 = 40

Again, we get 40 yards for the missing side!

Before you practice on your own, let's look at one more example:

basketball court

This time we have a basketball court with 4,700 square feet of new hardwood flooring inside the bounds. The width of the court is 50 feet. Find the missing length of the basketball court.