Area & Perimeter

Perimeter is the distance around the outside of a shape. Area is the amount of surface inside a shape. Both are used every day in construction, design, and sports.

Perimeter

Add up all the side lengths to find the perimeter.

Rectangle

P = 2 × (length + width)
A rectangle 8 cm long and 5 cm wide:
P = 2 × (8 + 5) = 2 × 13 = 26 cm

Irregular Shape

Just add every side: 4 + 6 + 3 + 5 + 2 + 7 = 27 units

Units of perimeter are always linear: cm, m, ft, in — never squared.

Area

Area is measured in square units (cm², m², ft²).

ShapeFormula
RectangleA = length × width
SquareA = side × side = side²
TriangleA = ½ × base × height

Rectangle: 10 m by 4 m

A = 10 × 4 = 40 m²

Triangle: base 6 cm, height 5 cm

A = ½ × 6 × 5 = 15 cm²

Real-World Applications

Area and perimeter show up in everyday problems.

Fencing a yard (Perimeter)

A yard is 20 ft × 15 ft. How much fencing?
P = 2 × (20 + 15) = 2 × 35 = 70 ft of fencing.

Carpet for a room (Area)

A room is 12 ft × 10 ft. How much carpet?
A = 12 × 10 = 120 ft² of carpet.

Watch out! Perimeter uses the same unit (ft, cm). Area uses the unit squared (ft², cm²). Always include the right unit in your answer.

Quick Quiz

Test what you just learned. Choose the best answer for each question.