The area formulas for rectangles, triangles, circles, trapezoids

Area shows up any time you're covering, painting, tiling, seeding or fencing a flat surface. Almost every real shape you'll measure at home reduces to one of four: a rectangle, a triangle, a circle or a trapezoid — and each has exactly one formula.

Rectangle: width × height

The simplest one: multiply the two sides. A room measuring 12 ft by 15 ft is 12 × 15 = 180 square feet.

Triangle: ½ × base × height

Half the base times the height — the height being the straight-line distance from the base up to the opposite point, not the length of a slanted side. A triangular garden bed with a 10 ft base and a 7 ft height: 0.5 × 10 × 7 = 35 square feet.

Circle: π × r²

Square the radius, then multiply by π (about 3.14159). A circular patio with a 6 ft radius: π × 6² = π × 36 = 113.097336, which rounds to 113.10 square feet. The radius is half the diameter — if you measured straight across the patio at 12 ft, the radius going into the formula is 6, not 12.

Trapezoid: (a + b) ÷ 2 × height

Average the two parallel sides, then multiply by the height between them. A deck shaped like a trapezoid with parallel edges of 8 ft and 12 ft, 5 ft apart: (8 + 12) ÷ 2 × 5 = 10 × 5 = 50 square feet.

A real example: an L-shaped room

Shapes that aren't one of the four still work — split them into pieces that are. An L-shaped room is two rectangles: a 12 ft × 15 ft section (180 sq ft) plus a 6 ft × 8 ft section (48 sq ft). Add the pieces: 180 + 48 = 228 square feet total. This is the same trick behind every irregular floor plan — decompose it into rectangles and triangles, find each area, then add.

What area doesn't tell you

Area is not perimeter — a long thin rectangle and a near-square one can share the same area while needing very different lengths of fencing or trim around the edge. And area alone doesn't account for waste: cutting tile or flooring to fit a room's actual edges (especially an L-shape or anything with angles) uses more material than the bare square footage, which is why installers commonly buy extra rather than the exact number the formula produces.

Run your own numbers

The free Area of Shapes calculator computes all four — rectangle, triangle, circle and trapezoid — from whichever measurements you enter, entirely on your device.