Area and Perimeter

What Is Perimeter?#

Perimeter is the total distance around the outside of a shape. Think of it as the length of the fence you would need to enclose a garden, or the length of trim you would need to go around the edge of a picture frame.

How to Calculate Perimeter#

To find the perimeter of any shape, add up the lengths of all its sides.

Perimeter = sum of all side lengths

Example: Perimeter of a Rectangle#

A rectangle has two pairs of equal sides:

• Two long sides (length)
• Two short sides (width)

Example: A rectangle with length = 8 cm and width = 5 cm.

Perimeter = 8 + 5 + 8 + 5 = 26 cm

Or use the formula: Perimeter = 2 × (length + width) = 2 × (8 + 5) = 2 × 13 = 26 cm

Example: Perimeter of a Square#

A square has four equal sides. If each side is 6 cm: Perimeter = 6 + 6 + 6 + 6 = 4 × 6 = 24 cm

Example: Perimeter of an Irregular Shape#

For shapes that are not regular, add all the sides:

A shape with sides 4 cm, 7 cm, 3 cm, 6 cm, 2 cm: Perimeter = 4 + 7 + 3 + 6 + 2 = 22 cm

Units of Measurement#

Perimeter is measured in linear units (units of length):

• Centimeters (cm)
• Meters (m)
• Inches (in)
• Feet (ft)

Always include the unit when you write your answer!

Real-Life Perimeter Problems#

• A classroom is 10 m long and 8 m wide. How much baseboard trim is needed? Perimeter = 2 × (10 + 8) = 2 × 18 = 36 m of trim

• A picture frame around a 12-inch × 9-inch photo. How much frame material? Perimeter = 2 × (12 + 9) = 2 × 21 = 42 inches