Area and Perimeter: How to Measure the Space Around and Inside a Shape

Ask around or inside

If you were putting a fence around a garden, you would need the perimeter. If you were spreading mulch over the garden, you would need the area. Draw a quick outline or shade the interior before you reach for a formula.

Perimeter uses linear units such as inches, feet, or meters. Area uses square units such as square inches, square feet, or square meters because two dimensions are being multiplied.

Rectangles use length times width

A rectangle with length 8 meters and width 3 meters has area 8 × 3 = 24 square meters. Its perimeter is 8 + 3 + 8 + 3 = 22 meters, or 2(8 + 3).

The same formula works for a square because its length and width are equal. A square with side 5 centimeters has area 25 square centimeters and perimeter 20 centimeters.

Triangles are half a matching rectangle

The area of a triangle is one half times base times height: A = 1/2bh. The height is the perpendicular distance from the base to the opposite vertex, not always the slanted side.

For base 10 inches and height 6 inches, the area is 1/2 × 10 × 6 = 30 square inches. Label the base and the perpendicular height before substituting numbers.

Circles need radius or diameter

The circumference is the distance around a circle: C = 2πr or πd. The area is inside the circle: A = πr². Radius runs from the center to the edge, while diameter crosses the whole circle.

If the diameter is 12 units, the radius is 6 units. Use the radius in the area formula and keep π until the final step if an exact answer is useful.

Estimate before you calculate

A rectangle 8 by 3 should have an area near 24, not 24 square meters if the side lengths were measured in centimeters. Check the size and the unit before rounding. A sensible estimate catches a surprising number of formula mix-ups.