Perimeter

Perimeter is the distance around the boundary of a two-dimensional shape. In geometry, it is the total length of the boundary, obtained by summing the lengths of all edges along the boundary. The perimeter measures how far the boundary stretches and is distinct from the area, which measures the size of the interior.

For polygons, the perimeter is the sum of the lengths of all sides. A rectangle with length l and width w has perimeter P = 2(l + w); a square with side s has P = 4s. For regular polygons with n equal sides of length s, the perimeter is P = n s. For irregular polygons, the perimeter is the sum of each side length.

Circles do not have edges but have a circumference, the analogue to a perimeter. The circumference is C = 2πr or C = πd, where r is the radius and d is the diameter. The constant π relates a circle’s circumference to its diameter.

Perimeter can be measured directly with a ruler or measuring tape for physical objects or computed from coordinates by summing the lengths of boundary segments in a digital model. If a shape is scaled by a factor k, its perimeter increases by the same factor k.

Etymology: the term perimeter comes from Greek peri metron, around measure. In practical use, perimeter appears in fields such as architecture, land surveying, and computer graphics, where it describes boundary length, while area concerns the size of the interior.