Perimeter of a square

Here you will learn how to find the perimeter of a square, including what the perimeter is, how to calculate it and how to solve perimeter word problems.

Students will first learn how to find perimeter as part of measurement and data in 3 rd grade.

What is perimeter of a square?

The perimeter of a square is the total distance around the outside of the square.

For example,

Perimeter is measured in units. Each side of the square is one unit.

The perimeter of the square is found by counting the units on each side of the square. You can do this by starting at a vertex and counting each unit until you arrive back at the vertex.

There are 16 units around the outside of the square, so the perimeter is 16 units.

Notice the perimeter can also be calculated by adding the length of each side.

4 + 4 + 4 + 4 = 16 , so the perimeter is 16 units.

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter.

4 \text { units } \times 4=16 \text { units }

The general perimeter of a square formula is \, 4 \, \times \text { side length } or \, 4s .

What is perimeter of a square?

Common Core State Standards

How does this relate to 3 rd grade math?

• Grade 3 – Measurement and data (3.MD.D.8)
  Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

How to find the perimeter of a square

In order to calculate the perimeter of a square:

1. Add all the side lengths.
2. Write the final answer with the correct units.

Perimeter of a square examples

Example 1: gridded square

What is the perimeter of the square?

1. Add all the side lengths.

This side of the square is 3 units. This means every side of the square is 3 units.

To find the perimeter (the total distance around the square), add all the side lengths:

3 + 3 + 3 + 3 = 12

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 3 \times 4=12.

2Write the final answer with the correct units.

There are no specific units given, so they are just labeled ‘units.’

The perimeter of the square is 12 units.

Example 2: gridded square

What is the perimeter of the square?

Add all the side lengths.

This side of the square is 5 units. This means every side of the square is 5 units.

To find the perimeter (the total distance around the square), add all the side lengths:

5 + 5 + 5 + 5 = 20

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 5 \times 4=20 .

Example 3: non-gridded square

What is the perimeter of the square?

Add all the side lengths.

One side of the square is 7 feet. This means every side of the square is 7 feet.

To find the perimeter (the total distance around the square), add all the side lengths:

7 + 7 + 7 + 7 = 28

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 7 \times 4=28 .

Example 4: non-gridded square

What is the perimeter of the square?

Add all the side lengths.

One side of the square is 13 {~cm} . This means every side of the square is 13 {~cm} .

To find the perimeter (the total distance around the square), add all the side lengths:

13 + 13 + 13 + 13 = 52

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 13 \times 4=52 .

Example 5: perimeter word problem

Nya has a square shaped garden. She wants to put a fence around the garden. If one side of the garden is 16 feet, how many feet of fencing does she need to surround the garden?

Add all the side lengths.

One side of the square is 16 {~ft} . This means every side of the square is 16 {~ft} .

To find the perimeter (the total distance around the square), add all the side lengths:

16 + 16 + 16 + 16 = 64

Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 16 \times 4= 64.

Example 6: given perimeter – find missing side length

The perimeter of the square is 44 {~m} . What are the side lengths?

Add all the side lengths.

Remember, all the sides of the square are congruent (equal).

So, the perimeter is the same number added 4 times:

? \; + \; ? \; + \; ? \; + \; ? = 44 \, m

Another way to think about it is ? \times 4=44.

Since 11+11+11+11= 44 and 11 \times 4= 44 , the side length of the square is 11 .

Teaching tips for the perimeter of a square

• Use worksheets that have a mixture of gridded or non-gridded squares and word problems (with and without a visual), so students can practice all perimeter solving strategies. This also challenges them to decide which strategies are most useful in different circumstances.

• Encourage students to look for patterns and extend patterns when finding the area of a square. Students are never too young to notice relationships and generalize patterns. This will also help them make sense of the formula 4 s .

Easy mistakes to make

• Thinking the order of adding the sides matters
  It doesn’t matter the order in which the sides of the shape are added, because of the commutative property of addition. As long as all sides are added only once, they can be added in any order.

• Confusing the formulas or solving strategies for perimeter with area
  It is easy to confuse these two concepts, especially when first learning them. Remember that perimeter is the measurement of the length around a square (one-dimensional) and area is the measurement of the space within a square (two-dimensional).

• Adding uncommon units
  Side lengths must be in the same units before they can be added. This means the unit squares must be the same size or the lengths given must all be in the same unit (for example, all measurements given are in {~cm} ). If the sides are shown in different units, convert them to be a common unit before adding.

Related perimeter lessons

• Perimeter
• How to find perimeter
• Perimeter of a rectangle
• Perimeter of a triangle

The next lessons are

• Symmetry
• Angles in polygons
• Congruence and similarity
• Prism shape

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