What you will learn
- Explain that perimeter is the distance around a shape.
- Count or add to find the perimeter of regular and irregular shapes.
- Compare perimeters and solve perimeter problems.
Walk all the way around the outside of a field and you have walked its perimeter. Perimeter is the distance around a shape. It is not the space inside. The space inside is called area, and that is a later lesson. In this lesson you will measure and calculate perimeters, compare them and use them in problems.
What is perimeter?
The perimeter is the total length of the sides. You can pace it, measure it with a ruler or a tape, or add the side lengths.
On a grid, count the outside edges of the squares. A block that is 3 squares long and 2 squares wide has 3 + 3 + 2 + 2 = 10 outside edges. Its perimeter is 10 units.
3 by 2 squares: perimeter 10 units
Worked example 1
A shape on a grid is 4 squares long and 1 square wide. What is its perimeter in units?
Show me how
The two long sides are 4 and 4.
The two short sides are 1 and 1.
4 + 4 + 1 + 1 = 10 units.
Regular shapes
A regular shape has all its sides the same length. Multiply the length of one side by the number of sides.
square: 4 × 5 cm = 20 cm
regular hexagon: 6 equal sides
Worked example 2
Each side of a regular pentagon is 7 cm. What is the perimeter?
Show me how
A pentagon has 5 sides.
The sides are equal, so multiply.
5 × 7 cm = 35 cm.
A square is a regular shape, so its perimeter is 4 times one side. A square of side 9 cm has perimeter 36 cm.
Shapes with different sides
If the sides are not all the same, add every side. Do not multiply length by width. That product is not the perimeter.
8 + 3 + 8 + 3 = 22 cm
5 + 6 + 7 = 18 cm
On a rectangle the opposite sides match. If you know the length and the width, the perimeter is length + width + length + width. That is the same as 2 × (length + width).
You can work backwards. If the perimeter of a rectangle is 26 cm and the length is 9 cm, then length + width = 13 cm, because 26 ÷ 2 = 13. The width is 13 − 9 = 4 cm.
Watch out! A common mistake
A common slip is to multiply the length by the width and call that the perimeter. 8 cm by 3 cm has area 24 square centimetres, but its perimeter is 8 + 3 + 8 + 3 = 22 cm. Add the way around. Do not multiply the two sides.
Worked example 3
A garden bed is a rectangle 9 cm by 4 cm on a plan. What is the perimeter of the rectangle on the plan?
Show me how
Add all four sides: 9 + 4 + 9 + 4.
Or do 2 × (9 + 4) = 2 × 13.
The perimeter is 26 cm.
Compare and solve
To compare perimeters, work out each one, then compare the numbers. The units must be the same. Two shapes can look different and still have the same perimeter. A long thin rectangle can have a longer perimeter than a square that looks bigger inside.
perimeter 16 cm
perimeter 12 cm
Worked example 4
Fencing costs 10 dollars a metre. A rectangular yard needs 8 m + 5 m + 8 m + 5 m of fence. What is the perimeter, and what does the fence cost?
Show me how
Perimeter = 8 + 5 + 8 + 5 = 26 m.
Cost = 26 × 10 dollars = 260 dollars.
The perimeter is 26 m and the fence costs 260 dollars.
Try it
TRY ITPerimeter lab
Count grid perimeters, add sides, find a missing side, compare two shapes and solve a problem.
Let’s practise
Work out each one in your copybook. Open Hint if you are stuck, then open Show answer to check your working.
1. What is the perimeter, in your own words?
Hint
Think of walking around the outside.
Show answer
The perimeter is the distance around a shape.
2. A square tile has sides of 8 cm. What is its perimeter?
Hint
A square has 4 equal sides.
Show answer
32 cm
3. A rectangle is 10 cm long and 4 cm wide. What is its perimeter?
Hint
Add all four sides, or double the length plus the width.
Show answer
28 cm
4. A triangle has sides 5 cm, 5 cm and 6 cm. What is its perimeter?
Hint
Add the three sides.
Show answer
16 cm
5. A rectangle has perimeter 20 cm and length 6 cm. What is the width?
Hint
Half of 20 is the length plus the width.
Show answer
4 cm
6. A shape on a grid is 2 squares by 2 squares. What is its perimeter in units?
Hint
Count the outside edges.
Show answer
8 units
7. Which has the greater perimeter: a 5 cm square, or a rectangle 8 cm by 3 cm?
Hint
Work out both perimeters.
Show answer
The rectangle. Its perimeter is 22 cm. The square is 20 cm.
8. Edging for a notice board is 12 m and costs 5 dollars a metre. What is the cost?
Hint
Multiply the length by the price of one metre.
Show answer
60 dollars
Quiz
Lesson quiz: 10 questions
Answer every question, then press Check my answers. Score 8 or more to earn the Perimeter Pro badge.
Perimeter: worksheet
Name: ____________________ Date: ______________
Part A: Let’s practise
1. What is the perimeter, in your own words?
2. A square tile has sides of 8 cm. What is its perimeter?
3. A rectangle is 10 cm long and 4 cm wide. What is its perimeter?
4. A triangle has sides 5 cm, 5 cm and 6 cm. What is its perimeter?
5. A rectangle has perimeter 20 cm and length 6 cm. What is the width?
6. A shape on a grid is 2 squares by 2 squares. What is its perimeter in units?
7. Which has the greater perimeter: a 5 cm square, or a rectangle 8 cm by 3 cm?
8. Edging for a notice board is 12 m and costs 5 dollars a metre. What is the cost?
Part B: Quiz
1. Perimeter is
(a) the space inside a shape
(b) the distance around a shape
(c) the number of corners
(d) the mass of a shape
2. A square has sides of 6 cm. What is the perimeter in centimetres?
3. A rectangle is 8 cm by 3 cm. What is the perimeter in centimetres?
4. Multiplying length by width gives the perimeter.
True or False? Circle one: True / False
5. A regular hexagon has sides of 4 cm. Its perimeter is
(a) 24 cm
(b) 10 cm
(c) 8 cm
(d) 16 cm
6. A rectangle is 7 cm long and its perimeter is 24 cm. What is the width in centimetres?
7. Which perimeter is the greatest?
(a) a square of side 3 cm
(b) an equilateral triangle of side 4 cm
(c) a rectangle 6 cm by 2 cm
(d) a square of side 2 cm
8. Two different shapes can have the same perimeter.
True or False? Circle one: True / False
9. Fencing costs 10 dollars a metre. A garden needs 9 m of fence. How many dollars does the fence cost?
10. To find the perimeter of a shape whose sides are different lengths, you
(a) multiply the sides together
(b) count the corners only
(c) add every side
(d) multiply length by width
Answers (for the adult)
Part A
1. The perimeter is the distance around a shape.
2. 32 cm
3. 28 cm
4. 16 cm
5. 4 cm
6. 8 units
7. The rectangle. Its perimeter is 22 cm. The square is 20 cm.
8. 60 dollars
Part B
1. (b) the distance around a shape
2. 24
3. 22
4. False
5. (a) 24 cm
6. 5
7. (c) a rectangle 6 cm by 2 cm
8. True
9. 90
10. (c) add every side
Recap
- Perimeter is the distance around a shape, not the space inside.
- On a grid, count the outside edges.
- For a regular shape, multiply one side by the number of sides.
- If the sides differ, add every side. On a rectangle you can do 2 × (length + width).
- Compare perimeters only after both are in the same unit.
Words to know
- perimeter
- The distance around a shape.
Example: The perimeter of the yard is 26 m. - distance around
- Another way to say perimeter.
Example: Walk the distance around the field. - regular shape
- A shape with all sides the same length.
Example: A square is regular, so the perimeter is 4 times one side. - unit
- The measure you are counting, such as cm or m.
Example: Do not compare 20 cm with 20 m.
Try it at home
- Pace around the kitchen table and around a rug. Which perimeter took more paces?
- Measure the four sides of a copybook with a ruler, add them, and write the perimeter in centimetres.
Test tips
Tips for class tests
- Sketch the shape and write a number on every side before you add. A missed side is the usual error.
- If it is regular, multiply. If it is not, add.
- Do not multiply length by width when the question asks for the perimeter.
For parents and teachers
After this lesson, your child should be able to:
- explain perimeter as the distance around a shape and tell it apart from the space inside;
- measure or calculate the perimeter of regular and irregular shapes, including a missing side of a rectangle;
- compare perimeters and solve perimeter problems that use length and money.
Keep area out of the calculation for now. If a child multiplies length by width, ask them to point to the path around the shape and add that path instead. Area is the next measurement idea, in a later lesson.
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Next: Mass: Kilograms and Grams – Standard 3 Maths
Course: Standard 3 Maths
Updates
2026/11/06
– Published this lesson and updated the lesson navigation.
2026/11/05
– First version of this lesson.
Attributions to media used in this post:
Peak to Peak Charter School soccer field and running track, Lafayette, Colorado, USA – 2025.jpg – Mikepascoe – CC0 1.0 (via Wikimedia Commons)
© 2026 Vedesh Kungebeharry. All rights reserved.
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