The image above is a pentagon.

To compute the area of a pentagon, one essential parameter is needed and this parameter is length of side (a).

The formula for calculating the area of a pentagon:

A = a^{2}√^{(5(5 + 2√5)} / _{4}

Where;

A = Area of the pentagon

a = length of side

Let’s solve an example;

Find the area of the pentagon when the length of side is 30 cm.

This implies that;

a = length of side = 30 cm

A = a^{2}√^{(5(5 + 2√5)} / _{4}

A = 30^{2}√^{(5(5 + 4.47)} / _{4}

A = 900√^{(5(9.47)} / _{4}

A = 900√^{47.36} / _{4}

A = 900√11.84

A = 900 x 3.44

A = 3096

Therefore, the **area of the pentagon** is **3096 cm ^{2}.**

**Calculating the length of side using the area of the pentagon.**

a = √(^{4A} / _{√5(5 + 2√5)})

Where;

a = length of side

A = Area of the pentagon

Let’s solve an example;

Find the length of side with an area of 150 cm^{2}.

This implies that;

A = Area of the pentagon = 150 cm^{2}

a = √(^{4A} / _{√5(5 + 2√5)})

a = √(^{4 x 150} / _{√5(5 + 1.148)})

a = √(^{600} / _{√5(6.148)})

a = √(^{600} / _{√30.74})

a = √(^{600} / _{5.54})

a = √108.30

a = 10.41

Therefore, the **length of side** is **10.41 cm.**