How to Find the Missing Side When You Know the Perimeter
In the last lesson, we learned that:
Perimeter is the length, or distance, around 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 the shape of the block.
We see that the block is a rectangle.
A rectangle has 4 sides. We need to add the length of all the sides:
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.
Find the Missing Side
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.
Tip: Think about it. You know one part and the total. To find the missing part, you subtract the part you know from the total.
22 - 14 = 8
✅ The length of the missing side is 8 ft.
5 + 2 + 2 + 5 + 8 = 22
Yes, we got the right perimeter, which means we found our answer!
Missing Sides in a Rectangle
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 if we got the right answer:
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!
Missing Sides in a Square
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.
👉 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!
Now, try the practice! 💪 You'll learn more and remember for longer.