# Regular Hexagon Formula

A polygon having six sides is known as a hexagon. Before we begin with the regular hexagon formula, let us first recall its definition. If all the sides of a hexagon are equal and angles are the same then the hexagon is called a regular hexagon. A regular hexagon has a total number of 9 diagonals. The sum of all interior angles of a regular hexagon is 720 degrees. Also, each interior angle is 120 degrees. A regular hexagon has an exterior angle is of 60 degrees and the sum of all exterior angles is 360 degrees. The regular hexagon formula is used to calculate its area, perimeter, of a regular hexagon.

## What Is Regular Hexagon Formula?

The regular hexagon formula is used to calculate its area, perimeter, and diagonals of a regular hexagon. Let’s say, each side of a regular hexagon is named s. To find the area, perimeter, and diagonals of a regular hexagon we use the following regular hexagon formulas.

- To find the area of a hexagon we use the following formula.

Area of regular hexagon formula = (3√3 × s^{2})/2 - To find the perimeter of a hexagon we use the following formula.

The perimeter of hexagon = 6s - To find the number of diagonals of a hexagon we use the following formula.

Number of Diagonals = n(n-3)/2

Where,

s = side length

n = number of sides

## Solved Examples Using Regular Hexagon Formula

**Example 1:** Calculate the perimeter and area of a regular hexagon having a side equal to 4 cm.

**Solution:**

To Find: Perimeter and area

Given: s = 4cm.

Using the regular hexagon formula for perimeter

Perimeter(P) = 6s

P = \(6 \times 4\)

P = 24 cm

Using the regular hexagon formula for area

\(\text{Area of hexagon} =\dfrac{(3\sqrt{3} \text s^2)}{2}\)

= \(\dfrac{(3\sqrt{3} \times 4^2)}{2}\)

= 41.56 cm^{2}

**Answer:** Perimeter and area of the hexagon are 24 cm and 41.56 cm^{2}.

**Example 2:** A hexagonal board has a perimeter equal to 12 cm. Find its area.

**Solution:**

To Find:** ** Area of the hexagon.

Given: Perimeter = 12 cm.

The perimeter of hexagon = 6s

12 = 6 s

s = 2cm.

Using the regular hexagon formula for Area,

\(\text{Area of hexagon} =\dfrac{(3\sqrt{3} \text s^2)}{2}\)

=\(\dfrac{(3\sqrt{3} \times 2^2)}{2}\)

=10.39 cm^{2}

**Answer:** Area of hexagonal board is 10.39 cm^{2}.