Perimeter: Find the Missing Side

In the last lesson we learned that:

Perimeteris thelength or distancearound a shape.

Let's say you want to ride your bicycle around your block.

How far do you have to ride?

To know the answer, you have to find your block's **perimeter.**

To find its perimeter, we start by **taking note of shape** of the block.

We see that the block is a rectangle.

A rectangle has 4 sides. We need to **know the length of all the sides:**

- Side 1 - 2 miles

- Side 2 - 1 mile

- Side 3 - 2 miles

- Side 4 - 1 mile

Now, we **add all lengths**.

2 + 1 + 2 + 1=6

The sum of all the sides is 6. But it's not just 6.

✅ It should be **6 miles.** The unit of length is very important.

Look at the shape below.

The **length of 1 side is missing**.

Can you find the length of the missing side?

👉 Let's start with what we know about this shape.

- This shape has 5 sides.

- Its perimeter is 22 ft.

The lengths of the other sides are 5 ft, 2 ft, 2 ft, and 5 ft.

Since **perimeter **is the length around a shape, this means that...

if we **add all the known sides** and the missing side, we'll get 22.

5 + 2 + 2 + 5+?=22

We can **simplify **this equation by adding all the known sides first.

5 + 2 + 2 + 5=14

So we can rewrite the equation as:

14+?=22

How many more do we need to make 22?

**Subtract** the sum of the known sides from the perimeter to find the length of the missing side.

22-14=8

✅ The length of the missing side is **8 ft**.

Let's check:

5 + 2 + 2 + 5 + 8=22

Our answer is correct!

This rectangle has 3 missing sides.

Only the perimeter and the length of one of its side are known.

How do we **find the length of the other sides**?

😃 We start with what we know.

We know **opposite sides **of a rectangle **have equal lengths**.

If one of the longer sides is 9 cm, then the other side is also 9 cm.

Now we only have **two **missing sides which are also **opposite sides**.

Since they are opposite sides, their lengths are also the same.

Let's write an equation for the numbers that we already have:

9 + 9 + ? + ?=30

👉 Let's add the 2 nines.

9 + 9=18

And simplify the equation:

18+?=30

To find the missing parts (**?**), subtract the part you know (**18**) from the whole (**30**):

30-18=12

😺 The total length of the 2 missing sides is** 12**.

We have to **divide 12 by 2** to get the length of each missing side.

12÷ 2 =6

✅ Each missing side is **6 cm long**!

Let's check:

9 + 9 + 6 + 6=30

We've got it right! ✊

So what did we learn?

If we know the **perimeter **of a **rectangle,** and the length of **just one side**, you can figure out the other three sides on your own!

Here we have a square.

Its perimeter is **48 inches**.

But **all the sides are missing.**

How do we find the missing sides?

Let's think about what we know about squares.

A **square **has 4 **equal **sides.

Equal means the same.

😃 This means that the length of the sides of this shape are the same.

👉 So we can just** divide** the perimeter by 4, then we'll have the length of each side.

48 inches ÷ 4 sides=?

48 ÷ 4=12

✅ The length of each side is **12 inches**.

If we add the length of the 4 sides together...

12 in + 12 in + 12 in + 12 in=48 in

... we get the perimeter again, 48 inches!

Great work!

You can try practice now! 💪

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