A perimeter is the total length of the boundary of any closed shape. It is the distance around a two-dimensional shape and is measured in linear units of measurement like centimeters, meters, inches, or feet. To find the perimeter of a shape, you add together the lengths of all the sides. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications, such as determining the length of fence required to surround a yard or garden, or the amount of string wound around a spool related to the spools perimeter. The formulas to find the perimeter of some regular polygons are:
- Triangle Perimeter = a + b + c
- Square Perimeter = 4 × a (where a is the length of side)
- Rectangle Perimeter = 2 × (a + b)
- Quadrilateral Perimeter = a + b + c + d
- Circle Circumference = 2πr (where r is the radius)
- Sector Perimeter = r(θ+2) (where r is the radius and θ is the angle in radians)
- Ellipse Perimeter = very hard!
Perimeter is most closely linked to properties of shapes, 2D shapes, and 3D shapes, and is one of the most basic and important parts of geometry. It is taught as children begin to learn geometry, and they begin by learning to measure the perimeter of simple 2-D shapes in 3rd grade. Children will also measure and calculate the perimeter of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter. In 4th grade, children apply the perimeter formula for rectangles in real-world and mathematical problems.
