Perimeter

Perimeter is the total length of the lines that form the boundary of a two-dimensional geometric shape. It is a measure of length and is therefore measured in units of length such as meters, centimeters, or kilometers.

Perimeter is distinct from area. Area measures the space inside a shape, while perimeter measures only the boundary. Two shapes with the same area can have different perimeters.

Calculating the perimeter of rectilinear shapes

Any shape with straight sides—such as triangles, rectangles, or polygons—has a perimeter found by adding together the lengths of all its sides. A square with side length a has perimeter 4a. A rectangle with sides a and b has perimeter 2(a + b).

The circle

When a shape is curved, the perimeter is the length of its curved boundary. For a circle, the perimeter is called the circumference, and is calculated using the formula 2πr, where r is the radius (the distance from the center to the edge) and π is the mathematical constant approximately equal to 3.14159.

Applications

Perimeter is used in everyday tasks: measuring the length of fencing needed for a field, calculating the amount of trim for a building's edge, and planning roads that border an area. Engineers and designers use it to determine how much material is needed for the boundary of an object.

The relationship between perimeter and area

For a given perimeter, the circle is the shape with the largest area. This fact is known as the isoperimetric problem and is important in geometry and mathematical analysis.