Perimeters

The perimeter of a shape is the total length of all of its sides. It is the distance around the outside of a figure or shape.

Units of Perimeter
The units used for measuring perimeters are the units of length used for giving the dimensions of the shape. Remember these units must be the same before you add them together. The perimeter of a circle is called its circumference and is covered in Circles.

Perimeter Formulae
The small lines on the sides of shapes show that the lengths of the sides are equal and thearrows show that the lines are parallel.

Shape
Name
Perimeter
Perimeter_01.gif
Square

P = 4 × l = 4l
Perimeter_02.gif
Rectangle

P = 2b + 2h
Perimeter_03.gif
Triangle

P = a + b + c

Perimeter_04.gif
Parallelogram

P = 2b + 2a

Perimeter_05.gif
Rhombus

P = Sum of all sides = 4b

Perimeter_06.gif
Trapezium

P = Sum of all sides

= a + b + c + d


Perimeter of Irregular Shapes

For shapes different from those above simply add up the lengths of the given sides and try to find the lengths of sides that are not given. Remember that diagrams are often not drawn to scale.

Add the lengths!
Change the units!
First find the missing lengths !
Perimeter_07.gif Perimeter_08.gif Perimeter_09.gif

Add up the lengths of all of the sides.

Perimeter = 4 + 5 + 8 + 10 
= 27 cm

Change units to same type.

500 cm = 0.5 m
800 cm = 0.8 m

Perimeter = 1.2 + 1.4 + 0.5 + 0.8 
= 3.9 m

Calculate the lengths of the missing sides.

x = 16 − 8 − 5 = 3 mm
y = 20 − 9 + 2 = 13 mm

Perimeter 
= 20 + 16 + 13 + 5 + 2 + 3 + 9 + 8
= 76 mm