Area and Perimeter Formulas for Every Shape

Area tells you how much surface a flat shape covers, measured in square units like cm² or m². Perimeter tells you how far you'd walk if you traced its outline, measured in ordinary length units. Together they're two of the most commonly used measurements in math class, on a job site, and in everyday tasks like buying flooring or fencing a yard.

Square

A square's four sides are all equal, which keeps both formulas about as simple as geometry gets:

Area = s²
Perimeter = 4s

Square with side 6 cm:
Area = 36 cm² · Perimeter = 24 cm

Rectangle

A rectangle brings in two different measurements, length and width, instead of just one:

Area = length × width (l × w)
Perimeter = 2(l + w)

Rectangle 8 cm × 3 cm:
Area = 24 cm² · Perimeter = 22 cm

Triangle

Given a base b and the perpendicular height h measured straight up from it:

Area = (1/2) × b × h
Perimeter = a + b + c (sum of all three sides)

Triangle base = 10 cm, height = 6 cm:
Area = (1/2) × 10 × 6 = 30 cm²

No height to work with, just three side lengths? Heron's formula solves it without ever needing an angle or a height measurement:

s = (a + b + c) / 2 (semi-perimeter)
Area = √(s(s−a)(s−b)(s−c))

Sides 5, 6, 7: s = 9
Area = √(9 × 4 × 3 × 2) = √216 ≈ 14.7 cm²

Circle

For a circle with radius r, where the diameter is simply twice that, or 2r:

Area = πr²
Circumference = 2πr = πd

Circle r = 5 cm:
Area = π × 25 ≈ 78.5 cm²
Circumference = 2π × 5 ≈ 31.4 cm

Parallelogram

A parallelogram has two pairs of parallel sides, and like a rectangle, its area depends on the perpendicular height, not the length of the slanted side:

Area = base × perpendicular height (b × h)
Perimeter = 2(a + b)

Base = 9 cm, height = 4 cm: Area = 36 cm²

Trapezoid (Trapezium)

A trapezoid has just one pair of parallel sides, usually labeled bases a and b, plus a height h connecting them:

Area = (1/2)(a + b) × h

Parallel sides 5 cm and 9 cm, height 4 cm:
Area = (1/2)(5 + 9) × 4 = (1/2)(14)(4) = 28 cm²

Formulas at a Glance

Shape	Area	Perimeter
Square (side s)	s²	4s
Rectangle (l × w)	lw	2(l + w)
Triangle (b, h)	½bh	a + b + c
Circle (radius r)	πr²	2πr
Parallelogram (b, h)	bh	2(a + b)
Trapezoid (a, b, h)	½(a+b)h	a + b + c + d

Watch Your Units

Area always comes out in square units - measure your lengths in meters and the area lands in m². Perimeter stays in whatever unit you measured the sides in to begin with. If a problem mixes units, say some sides in cm and others in m, convert everything to one unit before calculating anything.

Calculating It Automatically

SolverCalc's geometry calculator handles area and perimeter for all the shapes above, with a live preview that updates as you type. Just enter the dimensions and the result appears instantly, no formula lookup required.

Area and Perimeter Formulas, Shape by Shape