Area of Regular Polygon Calculator

Lets first understand, what is a polygon and how we can calculate the areas of different polygons?

Polygon

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal circuit.

The segments of a polygonal circuit are called its edges or sides and the points where two edges meet are the polygon's vertices.

A simple polygon is one which does not intersect itself.

Pentagon

A pentagon is any five-sided polygon. The total sum of the internal angles in a simple pentagon is 540°.

Let the length of each side of the pentagon be \(a\) units,

then area of the pentagon is given by

$$A=\dfrac{a^2}{4}\sqrt{5(5+2\sqrt{5})}$$

Hexagon

A hexagon is any six-sided polygon. The total sum of the internal angles in a simple hexagon is 720°.

Let the length of each side of the hexagon be \(a\) units,

then area of the hexagon is given by

$$A=\dfrac{3\sqrt{3}}{2}a^2$$

Heptagon

A heptagon is any seven-sided polygon. The total sum of the internal angles in a simple heptagon is 900°.

Let the length of each side of the heptagon be \(a\) units,

then area of the heptagon is given by

$$A=\dfrac{7}{4}a^2\cot\left(\dfrac{180°}{7}\right)$$

Octagon

An octagon is any eight-sided polygon. The total sum of the internal angles in a simple octagon is 1080°.

Let the length of each side of the octagon be \(a\) units,

then area of the octagon is given by

$$A=2(1+\sqrt{2})a^2$$

Nonagon

A nonagon is any nine-sided polygon. The total sum of the internal angles in a simple nonagon is 1260°.

Let the length of each side of the nonagon be \(a\) units,

then area of the nonagon is given by

$$A=\dfrac{9}{4}a^2\cot\left(\dfrac{180°}{9}\right)$$

Decagon

A decagon is any ten-sided polygon. The total sum of the internal angles in a simple decagon is 1440°.

Let the length of each side of the decagon be \(a\) units,

then area of the decagon is given by

$$A=\dfrac{5}{2}a^2\sqrt{5+2\sqrt{5}}$$

For calculating areas of different regular polygons using above area of regular polygon calculator, you have to just write the values in the given input boxes and press the calculate button, you will get the result.