Geometry

Perimeter

Perimeter formulas for common 2D shapes: squares, rectangles, parallelograms, circles, triangles, and regular polygons.

Perimeter is the total length of a planar shape’s boundary, measured in linear units (metres, inches, and so on). For polygons it is the sum of side lengths. For a circle the analogous quantity is the circumference, 2πr. The formulas below cover squares, rectangles, parallelograms, circles, triangles, and regular polygons.

Perimeter is the total length of a closed boundary.

Square

Four equal sides of length a. Perimeter is four times the side:

Perimeter=4a

Rectangle

Sides a and b. Opposite sides are equal, so the perimeter is twice the sum of one of each:

Perimeter=2\left(a+b\right)

Parallelgram

Adjacent sides a and b. Opposite sides are equal, so the perimeter takes the same form as a rectangle. The slant angle does not enter:

Perimeter=2a+2b

Circle

Radius r. The circumference is 2π times the radius, the limiting case of a regular polygon as the number of sides grows without bound:

Perimeter=2\pi r

Triangle

Sides a, b, and c. Perimeter is their sum. No angle information is required:

Perimeter=a+b+c

Any Regular Pilygon

n equal sides of length s give a perimeter of ns, the sum of all sides. The general statement below covers irregular polygons as well:

Perimeter=Sum\text{ }of\text{ }the\text{ }sides