Quick answer: A rectangle 8 m long and 5 m wide has an area of 8 × 5 = 40 m² and a perimeter of 2 × (8 + 5) = 26 m.
How it's calculated
Rectangle: length × width. Square: side². Parallelogram: base × height. Triangle: ½ × base × height. Trapezoid: ½ × (sum of the parallel sides) × height. In each case the height is measured at right angles to the base.
Circle: πr². Ellipse: π × a × b, where a and b are the semi-axes (half the longest and shortest widths). Sector: ½ × r² × θ with the angle θ in radians, which equals (angle ÷ 360) × πr².
Area is in square units: metres give m². To convert, 1 m² = 10,000 cm² = 10.7639 ft². For a room with several parts, split it into rectangles and add the areas.
Worked examples
- Rectangle 8 × 5 m: 40 m², perimeter 26 m
- Trapezoid with sides 6 and 10, height 4: ½ × 16 × 4 = 32
- Sector, radius 5, angle 60°: ½ × 25 × 1.047198 = 13.089969
Frequently asked questions
How do I find the area of an L-shaped room?
Split it into two rectangles, find each area and add them.
Why is there no perimeter for a triangle or parallelogram?
Base and height do not fix the slanted sides, so the perimeter cannot be found from them. The triangle calculator gives it from the sides.
Is the ellipse perimeter exact?
No closed formula exists. Ramanujan's approximation used here is accurate to a tiny fraction of a percent for ordinary ellipses.
What about solids?
Use the volume calculator and the surface area calculator.
How many square metres is an 8 × 5 m room?
40 m², which is about 430.6 square feet.
How do I find a triangle's area without its height?
If you know all three sides, use Heron's formula. The triangle calculator does it for you; a 3-4-5 triangle comes out at 6.