Polygons are two-dimensional shapes, such as triangles and squares, that have three or more straight sides. Regular polygons are polygons whose sides are all the same length. Angles inside a polygon are interior angles. Angles formed by one side of the polygon and a line extending outside the polygon are exterior angles.

The formulas below describehow to find interior and exterior angles of a regular polygon with side n.

sum of interior angles\(= (n\ −\ 2)\ ×\ 180^\circ\)

measure of interior angle \(=\frac{n\ −\ 2}{n}\ ×\ 180^\circ\)

sum of exterior angles \(=360^\circ\)

measure of exterior angle \(=\frac{360^\circ}{n}\)

Perimeter is the distance around a shape. It can be determined by adding the lengths of all sides of the shape. Area is the amount of space a shape occupies. The area of an object is its length times its width and is measured in square units. For example, if a wall is 3 feet long and 2 feet wide, its area would be 6 square feet (ft^{2}).

The table below gives the formulas for the area and perimeter of basic shapes. To find the area and perimeter of a circle, use the constant pi (π = 3.14).

Area and Perimeter of Basic Shapes

Shape

Areas

Perimeter

Triangle

\(A = \frac{1}{2}bh\)

\(P = s_1\ +\ s_2\ +\ s_3\)

Square

\(A = s^{2}\)

\(P = 4s\)

Rectangle

\(A = l\ ×\ w\)

\(P = 2l\ +\ 2w\)

Circle

\(A = \pi r^{2}\)

\(C = 2\pi r\ (circumference)\)

An equilateral figure has sides that are all the same length. In an equiangular figure, all the angles have the same measurement. To find the length of a side in an equilateral figure, divide the perimeter by the number of sides. To find the measure of each angle, divide the sum of all the interior angles by the number of angles.