The perimeter of a shape is the length of its boundary. We add the length of every side to find the perimeter.

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Think of the small character walking all the way around the box shown below. The perimeter is what he walks around to get to back to where he started.

Hint: Perimeter and area are often taught at the same time and it can be easy to confuse one with the other. Think of a memory prompt to help remember which is which.

How about P for *perimeter*, P for *post* , Fence *posts* will go all the way around the *perimeter*.

First side | 4 cm |

Second side | 3 cm |

Third side | 4 cm |

Fourth side | 3 cm |

Total ( 4 + 3 + 4 + 3)= | 14 cm |

So what is the perimeter of the rectangle (the box) shown above?

It is 4 cm + 3 cm + 4 cm + 3 cm = 14 cm

**Perimeter of a Rectangle**

What do we know about a rectangle?

- It has 4 sides
- the opposite sides are equal so there are 2 sides of length and 2 sides of width
- The perimeter = ( 2 x length) + (2 x width) which is ..
- ..the same as 2 x (length + width)

Here are some examples

5 | |

4 |

2 x Length = 2 x 5 = 10

2 x Width = 2 x 4 = 8

Perimeter = 10 + 8 = 18

or

Length + Width = 5 + 4 = 9

Perimeter = 2 x 9 = 18

4 | |

3 |

2 x Length = 2 x 4 = 8

2 x Width = 2 x 3 = 6

Perimeter = 8 + 6 = 14

or

Length + Width = 4 + 3 = 7

Perimeter = 2 x 7 = 14

2 | |

6 |

2 x Length = 2 x 6 = 12

2 x Width = 2 x 2 = 4

Perimeter = 12 + 4 = 16

or

Length + Width = 6 + 2 = 8

Perimeter = 2 x 8 = 16

7 | |

3 |

2 x Length = 2 x 7 = 14

2 x Width = 2 x 3 = 6

Perimeter = 14 + 6 = 20

or

Length + Width = 7 + 3 = 10

Perimeter = 2 x 19 = 20

A quick way to find the perimeter of a rectangles is to add the length and width and then multiply by 2

**Perimeter of a Square**

A square is a type of rectangle so we can use the same method for calculating perimeter although there is an even easier way: since the 4 sides of a square are the same length, we just need to add the length 4 times. e.g. for a square with a side of 5 we have a perimeter of 5 + 5 + 5 + 5. Or, even more quickly, we can take the length and multiply by 4.

the length and multiply by 4.

5 | |

5 |

Perimeter = 5 + 5 + 5 + 5 = 20

or

Perimeter = 4 x Length

Perimeter = 4 x 5 = 20

**Perimeter of Polygons**

You can find out more about different types of polygons here.

**The perimeter of a polygon is the sum of the lengths of all its sides.** The example below shows an irregular hexagon with a perimeter = 20 cm (3 cm + 3cm + 3cm +3cm + 4cm + 4cm)

A polygon whose sides are equal is called a Regular Polygon. All angles of a Regular Polygon are also equal.

To find the perimeter of a regular polygon, multiply the length of the side by the number of sides.

Shape/ Description | Perimeter | |
---|---|---|

Pentagon5 equal-sided polygon |
Perimeter = 5 x length of side | |

Hexagon6 equal-sided polygon |
Perimeter = 6 x length of side | |

Heptagon7 equal-sided polygon |
Perimeter = 7 x length of side | |

Octagon8 equal-sided polygon |
Perimeter = 8 x length of side |

**Perimeter Worksheets**

Use the printable worksheets listed below to practice calculating perimeters.

- Perimeter - Rectangles and Squares
- Perimeter - Rectangular Shapes
- Perimeter - Rectangular Shapes
- Perimeter e.g. various polygons

You will find other printable geometry worksheets here.