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# Hexagon Formula

A polygon having six sides is known as a hexagon. There are few types of hexagons i.e, regular hexagon, irregular hexagon, and, concave hexagon. If all the sides of a hexagon are equal and angles are the same then the hexagon is called a regular hexagon. A 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 of 60 degrees and the sum of all exterior angles is 360 degrees. The hexagon formula is used to calculate its area and perimeter.

## What Is Hexagon Formula?

The hexagon formula is defined as a set of formulas to calculate the perimeter, area, and diagonals of the hexagon. The hexagon formulas apply directly to regular hexagons.

### Hexagon Formula

The hexagon formula can be written as:

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

Where,

- s = side length.

**Perimeter of hexagon: 6s**

Where,

- s = side length.

**Diagonals of a hexagon: 2s and √3s**

Where,

- s = side length

**Special Formula:** Area = 1/2×perimeter×apothem

Let us see the applications of the hexagon formula in the following solved examples.

## Derivation of Hexagon Formula

Consider a regular hexagon of side s. Then,

**Area of a hexagon**

- Divide the hexagon into small six isosceles triangles.
- Find the area of one of the triangles.
- Multiply by 6.

Thus, \(\dfrac{(3\sqrt{3} \text s^2)}{2}\)

**Perimeter of a hexagon**

- The perimeter of any polygon is the sum of all the side lengths.
- A regular hexagon has 6 sides. Thus, multiply the side length by 6.

Thus, the formula for the perimeter of a regular hexagon is given as, P=6×a

**Diagonal of a hexagon**

- In a hexagon, there are 6(6-3)/2 = 9 diagonals
- These nine diagonals form into six equilateral triangles.
- For longer diagonal, d = 2s, and for shorter diagonal, d = √3s, where s refers to the side of the hexagon.

Thus, the formula for the diagonal of a hexagon is given as, d = 2s, and √3s

## Solved Examples Using Hexagon Formula

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

**Solution:**

**To Find:** Perimeter and Area

**Given:** s= 4 units.

Using the hexagon formula for perimeter

Perimeter(P) = 6s

P = \(6 \times 4\)

P = 24 units

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 units^{2}

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

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

**Solution:**

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

Given: Perimeter = 12 inches.

The perimeter of hexagon = 6s

12 = 6 s

s = 2 inches.

Using the 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 inches^{2}

**Answer: The area of the hexagonal board is 10.39 inches ^{2}.**

**Example 3: Determine the side length of the regular hexagon whose perimeter is 24 units.**

**Solution:**

**To Find:** Side length of hexagon

**Given:** perimeter= 24 units.

Using the hexagon formula for perimeter

Perimeter(P) = 6s

24 = \(6 \times s\)

s = 24/6 units

= 4 units

**Answer:** The side length** of the hexagon is 4 units.**

## FAQs on Hexagon Formula

### What Is Hexagon Formula in Geometry?

The hexagon formula calculates the perimeter, area, and diagonals of the hexagon. The hexagon formulas apply directly to regular hexagons. The hexagon formulas are given as, Area of hexagon = \(\dfrac{(3\sqrt{3} \text s^2)}{2}\) and Perimeter of hexagon = 6s, where s = side length.

### What Is s in Hexagon Formula?

In hexagon formulas, Area of hexagon= \(\dfrac{(3\sqrt{3} \text s^2)}{2}\) and Perimeter of hexagon = 6s, s refers to the side of the regular hexagon.

### How To Use Hexagon Formula?

To use the hexagon formula for a given hexagon

- Step 1: Identify if the given hexagon is regular or irregular.
- Step 2: Identify the side of the regular hexagon.
- Step 3: Put the value in the appropriate formula, Area of hexagon = \(\dfrac{(3\sqrt{3} \text s^2)}{2}\) and Perimeter of hexagon = 6s

### What Is Hexagon Formula For Irregular Hexagon?

In the case of an irregular hexagon, divide the given hexagon into rectangles and right triangles and then find the area of each shape whereas to calculate perimeter, just add the lengths of all its sides.

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