Area Calculator
Calculate the area of common shapes: rectangle, triangle, circle, and trapezoid.
- Width10
- Height5
The rectangle's width and height sized up side by side — the area is the space they enclose together.
ƒShow your work
Area = width × height
- 1Area = 10 × 5 = 50
About the Area Calculator
Area calculations turn up constantly outside the classroom: figuring out how much flooring, paint, sod, or fabric to buy for a project, or checking a geometry homework answer against a known formula. Because different shapes need genuinely different formulas — a rectangle's is trivial, a trapezoid's is not — this calculator covers the shapes people actually run into most: rectangle, triangle, circle, and trapezoid.
It's built for the practical case as much as the classroom one — measure a room or a plot of land, pick the closest matching shape, and get an area you can take straight to a hardware store or materials calculator.
How it’s calculated
A rectangle's area is simply width × height — the most basic case, and the one every other formula ultimately relates back to. A triangle's area is half of that: ½ × base × height, because any triangle is exactly half of the rectangle (or parallelogram) that would enclose it.
A circle's area is πr², derived from the radius. A trapezoid — a four-sided shape with exactly one pair of parallel sides — uses ½ × (base₁ + base₂) × height, which is really just an averaging trick: it treats the trapezoid as the shape 'between' a rectangle made from the shorter parallel side and one made from the longer one.
Frequently asked questions
How do I find the area of an irregular shape?
Break it down into simpler shapes this calculator already covers — rectangles, triangles, circles, trapezoids — calculate each piece's area separately, then add them together (or subtract, for a cut-out section) to get the total.
What's the difference between area and perimeter?
Area measures the space enclosed inside a shape's boundary, in square units (like square feet). Perimeter measures the total length of the boundary itself, in linear units (like feet). They answer completely different questions — perimeter is how much fencing you need, area is how much sod fills the yard it encloses.
How do I convert square feet to square meters?
Multiply by 0.0929 (since 1 square foot equals about 0.0929 square meters) — note this isn't the same conversion factor as linear feet to meters, because it's the linear factor applied twice (squared), since area scales with the square of length.
Why does the trapezoid formula average the two parallel sides?
Because a trapezoid's width changes steadily from one parallel side to the other, its area works out to be the same as a rectangle built from the average of those two widths, times the height between them — that's exactly what ½ × (base₁ + base₂) × height computes.
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