A polygon with 5 sides is known as pentagon. The area of a pentagon is calculated by using 5 sides and the area of the triangle in them. In this calculator student can enter the side length of the given pentagon and the resultant area are would be displayed in sq.units. This calculator can be used only when all the sides of the pentagon are equal.

## How to Find the Area of a Pentagon

Area of a Regular Pentagon:

Step 1: Let 'd' be the sides of a regular pentagon

Step 2: Area of a Regular Pentagon = 5 $\times$ Area of Small triangle

Step 3: Area of one Triangle = $\frac{1}{2}$$\times base \ height = \frac{1}{2}$$\times d \times height$

Step 4: In  $\Delta XOD$, $\tan 36^{\circ}$ =   $\frac{Opposite\ side}{Adjacent\ side}$

=   $\frac{\frac{d}{2}}{height}$

Step 5: Height =  $\frac{d}{2\tan 36^{\circ}}$

Step 6: Area of Triangle = $\frac{1}{2}$$\times d \times$ $\frac{d}{2 \tan 36^{\circ}}$

= $\frac{d^{2}}{4 \tan36^{\circ}}$

Step 7:
Area of Regular Pentagon = $5 \times$ $\frac{d^{2}}{4\ tan 36^{\circ}}$

= $1.72 \times d^{2}$

= $1.72 \times (Side)^{2}$

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