Area Formulas

Area formulas give the amount of surface a two-dimensional shape covers, always in square units. The essentials are square A = s², rectangle A = l·w, triangle A = ½·b·h, and circle A = πr². The full table below covers every common 2D shape, each linking to an interactive explorer.

All 2D area & perimeter formulas

Shape	Area	Perimeter / circumference
Square	$A = s^2$	$P = 4s$
Rectangle	$A = l \cdot w$	$P = 2(l + w)$
Triangle	$A = \tfrac{1}{2} b h$ $A = \sqrt{s(s-a)(s-b)(s-c)}$	$s = \dfrac{a+b+c}{2}$ $P = a + b + c$
Right Triangle	$A = \tfrac{1}{2} a b$	$P = a + b + c$
Circle	$A = \pi r^2$	$C = 2\pi r$
Trapezoid	$A = \tfrac{1}{2}(a + b)h$
Parallelogram	$A = b h$	$P = 2(a + b)$
Rhombus	$A = \tfrac{1}{2} d_1 d_2$	$P = 4s$
Regular Polygon	$A = \tfrac{1}{2} a P$	$P = n s$

Worked examples

Rectangle 8 × 5: A = l·w = 8 × 5 = 40 square units.
Triangle base 10, height 6: A = ½·b·h = ½ × 10 × 6 = 30.
Circle radius 5: A = πr² = π × 25 ≈ 78.54.
Trapezoid parallel sides 4 and 8, height 5: A = ½(4 + 8)·5 = 30.

Variable glossary

a, b, cside lengths
l, w, hlength, width, height
rradius
ddiameter (d = 2r)
sside length or slant height
ℓslant height
bbase
Pperimeter
Ccircumference
Aarea
SAsurface area
Vvolume
θcentral angle (degrees)

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Frequently asked questions

What are the basic area formulas?

The core area formulas are: square A = s², rectangle A = l·w, triangle A = ½·b·h, circle A = πr², and trapezoid A = ½(a + b)h. Each measures the space a flat shape covers, in square units.

What is the difference between area and perimeter?

Area measures the surface a shape covers (in square units), while perimeter measures the distance around its edge (in linear units). A 3 × 4 rectangle has area 12 but perimeter 14.

How do you find the area of an irregular polygon?

Split it into triangles and rectangles, find each piece’s area, and add them up. For regular polygons, use A = ½·a·P, where a is the apothem and P the perimeter.