Area formulas for common shapes
| Shape | Area formula |
|---|
| Square | side² |
| Rectangle | length × width |
| Triangle | ½ × base × height |
| Circle | π × radius² |
| Trapezoid | ½ × (base₁ + base₂) × height |
| Parallelogram | base × height |
| Ellipse | π × semi-axis a × semi-axis b |
| Circle sector | (angle ÷ 360) × π × radius² |
Worked examples
- Rectangle: a 12 ft × 8 ft rug covers 12 × 8 = 96 square feet.
- Triangle: a sail with a 10 ft base and 15 ft height has an area of ½ × 10 × 15 = 75 square feet.
- Circle: a 14-inch pizza has a 7-inch radius, so its area is π × 7² ≈ 153.9 square inches.
- Trapezoid: a garden bed with parallel sides of 6 m and 4 m and a depth of 3 m covers ½ × (6 + 4) × 3 = 15 m².
Measuring tips
- Use one unit for every measurement of a shape, then convert the answer if needed.
- Remember that area units are squared: 1 square foot is 144 square inches, not 12.
- For triangles and parallelograms, measure the perpendicular height, not the slanted side.
Measuring a room for flooring? The square footage calculator adds several areas and includes waste and cost.
Last reviewed October 2026.
Frequently asked questions
What is area?
Area is the amount of flat space inside a 2D shape, measured in square units such as square inches, square feet or square meters. A 1-foot by 1-foot tile covers 1 square foot.
How do I find the area of a circle?
Multiply pi (about 3.14159) by the radius squared: A = πr². A circle with a radius of 5 cm has an area of about 78.54 cm². If you know the diameter, halve it to get the radius first.
Why is a triangle's area half of base × height?
Any triangle is exactly half of a parallelogram with the same base and height. Two copies of the triangle fit together to make that parallelogram, so the triangle gets half its area.
What is the height of a triangle or parallelogram?
The height is the straight-up distance from the base to the opposite point or side, measured at a right angle to the base. It is not the length of the slanted side.
How do I find the area of an irregular shape?
Divide it into simple shapes like rectangles and triangles, find each area, and add them together. Subtract any cut-out parts. For rooms and floors, the square footage calculator lets you add several areas at once.