Perimeter Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Perimeter.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The total distance around the outside of a two-dimensional shape, found by adding all its side lengths.

If an ant walked around the edge of a rectangle, perimeter is how far it walked.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Perimeter measures the distance around a shape.

Common stuck point: The procedure for perimeter is the easy part; the trap is multiplying length and width for a fence problem. Asking "Would I solve it by tracing the boundary?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Would I solve it by tracing the boundary?

Worked Examples

Example 1

easy
Find the perimeter of a rectangle with length 88 cm and width 55 cm.

Answer

P=26 cmP = 26 \text{ cm}

First step

1
Recall the perimeter formula for a rectangle: P=2l+2wP = 2l + 2w.

Full solution

  1. 2
    Substitute the values: P=2(8)+2(5)=16+10=26P = 2(8) + 2(5) = 16 + 10 = 26.
  2. 3
    The perimeter is 2626 cm.
The perimeter of any polygon is the total distance around its boundary. For a rectangle, opposite sides are equal, so we add two lengths and two widths.

Example 2

medium
A triangle has sides measuring 77 cm, 1010 cm, and 1212 cm. Find its perimeter.

Example 3

easy
Find the perimeter of an equilateral triangle with side length 1212 in.

Example 4

medium
A rectangle has perimeter 5454 m and length 2020 m. Find its width.

Example 5

medium
An isosceles triangle has perimeter 3434 cm. The base is 1010 cm. Find the length of each equal side.

Example 6

hard
A rectangular field has length 55 m more than its width and perimeter 7070 m. Find length and width.

Example 7

challenge
A regular hexagon and a square have equal perimeters. The hexagon's side is 66 cm. Find the square's side.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Find the perimeter of a square with side length 99 m.

Example 2

medium
The length of a rectangle is 33 m more than twice its width. If its perimeter is 4242 m, find the length and width.

Example 3

easy
Find the perimeter of a square with side length 66 cm.

Example 4

easy
Find the perimeter of a rectangle with length 99 in and width 44 in.

Example 5

easy
Find the perimeter of an equilateral triangle with side length 77 m.

Example 6

easy
A regular hexagon has each side 55 cm. What is its perimeter?

Example 7

easy
A triangle has sides 33, 44, and 55. Find its perimeter.

Example 8

easy
Find the perimeter of a rectangle with length 1212 and width 55.

Example 9

easy
An isosceles triangle has two equal sides of length 88 and a base of 55. Find its perimeter.

Example 10

easy
A square has perimeter 3232 cm. Find the side length.

Example 11

medium
A rectangle has perimeter 3030 and length 99. Find its width.

Example 12

medium
An L-shaped figure is formed by cutting a 2×32 \times 3 rectangle from the corner of a 6×56 \times 5 rectangle. Find the perimeter of the L-shape.

Example 13

medium
A regular pentagon has perimeter 4040 cm. Find each side length.

Example 14

medium
A rectangle has perimeter 2424 and its length is twice its width. Find the dimensions.

Example 15

medium
A garden is a rectangle 2020 m long and 1212 m wide. Fencing costs $8 per meter. How much does it cost to fence the garden?

Example 16

medium
A square and an equilateral triangle have the same perimeter. The square has side 66. Find the triangle's side.

Example 17

medium
A rectangle has perimeter 5050 and length 55 more than width. Find length and width.

Example 18

medium
A staircase shape is made of three squares each with side 22, stacked diagonally so each shares one edge with the next. Find the perimeter of the staircase shape.

Example 19

medium
A right triangle has legs 55 and 1212. Find its perimeter. (Hint: find the hypotenuse first.)

Example 20

challenge
A rectangle has integer length and width with perimeter 2020. What are all possible (length, width) pairs with length ≥\geq width? Which has the largest area?

Example 21

challenge
Two squares with side lengths 44 and 66 share one common side (the smaller's side lies along the larger's side). Find the perimeter of the resulting composite shape.

Example 22

challenge
A rectangle is cut by a straight line from one side to a non-adjacent side, dividing it into two pieces. The original rectangle has perimeter 3030 and the cut has length 77. What is the sum of the perimeters of the two pieces?

Example 23

easy
A square has side length 1010 cm. Find its perimeter.

Example 24

easy
Find the perimeter of a rectangle with length 77 m and width 33 m.

Example 25

easy
A regular pentagon has each side measuring 44 cm. Find its perimeter.

Example 26

easy
A rectangle has length 1111 ft and width 66 ft. Find its perimeter.

Example 27

medium
A regular octagon has perimeter 5656 cm. Find each side.

Example 28

medium
A quadrilateral has sides 88, 99, 1111, and 1414. Find its perimeter.

Example 29

medium
A right triangle has legs 99 and 1212. Find its perimeter.

Example 30

medium
A rectangular swimming pool measures 2525 m by 1212 m. How many meters of fencing are needed to enclose it?

Example 31

medium
A regular hexagon has perimeter 4848 in. Find each side.

Example 32

medium
A garden is a regular octagon, each side 3.53.5 m. Find the perimeter.

Example 33

medium
A trapezoid has parallel sides 77 and 1010 and non-parallel sides 55 and 66. Find its perimeter.

Example 34

medium
A rhombus has perimeter 5252 cm. Find each side.

Example 35

hard
An L-shape is formed by cutting a 3×43 \times 4 rectangle from the corner of a 10×810 \times 8 rectangle. Find the perimeter of the L-shape.

Example 36

hard
A right triangle has hypotenuse 1313 and one leg 55. Find its perimeter.

Example 37

hard
A regular polygon has perimeter 6060 cm and each side 55 cm. How many sides does it have?

Example 38

hard
A rectangle's length is 33 less than twice its width. Its perimeter is 5454. Find the dimensions.

Example 39

challenge
Fencing costs $12/m. A rectangular yard measures 1414 m by 99 m. Find the cost to fence it.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

additionshapes