Geometry · 5 min read
How to Calculate Area of Common Shapes
Rectangle, triangle, and trapezoid — count the square units inside
Area is the measure of a region in the plane: how many unit squares fit inside the boundary. This tutorial walks through A = ℓ w for a rectangle (the Area calculator), A = ½ b h for a triangle, and A = ½ (a + b) h for a trapezoid, an 8 × 5 worked example, and a playground that redraws the labeled figure as you switch shapes.
Written by the My Calculator Stack editorial team. About our methods
These identities assume positive side lengths in one length unit; area is then in that unit squared. The Area calculator on this site is the rectangle tool A = ℓ w. Triangle and trapezoid formulas here are teaching identities, not separate calculator pages.
1.What area is
Area answers how much surface a flat shape covers. Length and width are one-dimensional; their product (with the right factor for triangles and trapezoids) is two-dimensional. All edges in one formula must share a length unit — mix meters with inches and the square-unit count is meaningless. A circle uses π r² instead; that identity lives on the Circle calculator. A right triangle’s legs also appear in the Pythagorean theorem, which finds the hypotenuse rather than the area.
2.The formulas
A rectangle (or parallelogram sitting square to its base) is length times width: A = ℓ w. A triangle is half a parallelogram with the same base and height: A = ½ b h, where h is perpendicular to base b. A trapezoid has one pair of parallel sides a and b; average those bases and multiply by the perpendicular height: A = ½ (a + b) h. Height is never a slanted side.
\[ \begin{aligned}A_{\mathrm{rect}} &= \ell w \\A_{\mathrm{tri}} &= \tfrac12 bh \\A_{\mathrm{trap}} &= \tfrac12(a+b)h\end{aligned} \]
3.Worked example
Take length ℓ = 8 and width w = 5 — the same defaults as the Area calculator. Then A = 8 × 5 = 40 square units. A triangle with base 8 and height 5 is half of that rectangle: A = ½ × 8 × 5 = 20. A trapezoid with parallel sides 6 and 10 and height 4 is ½ (6 + 10) × 4 = 32.
\[ A=8\times 5=40 \]
4.Shape playground
Toggle rectangle, triangle, or trapezoid, then move the side sliders. The labeled figure updates with the current dimensions and the substituted area. This is a teaching widget — no favorites, no full calculator chrome. Open the Area calculator when you want the standalone rectangle tool.
Inline playground
Area A
40
A = 8 × 5 = 40
Teaching aid only — sides and heights must be positive and share one length unit.
Open the full Area calculator →5.Open the full calculator
The Area calculator uses A = ℓ w and the same 8 × 5 example, with How it works, FAQ, and related geometry tools on one page. Browse other geometry calculators if you need a circle, a volume, or the Pythagorean theorem next.
Try it yourself
Open the related calculator and put these formulas to work.