Area of Hexagon Formula

Introduction

The area of a hexagon is the space bounded by all of its sides. A Hexagon is a polygon with six sides and six angles. Regular hexagons are made up of six equilateral triangles and have six equal sides and six angles. There are several methods for calculating the area of a hexagon, whether it is an irregular hexagon or a regular hexagon.

There are several methods for calculating the area of a hexagon formula. The various methods are primarily determined by how you spit the hexagon. It can be divided into 6 equilateral triangles or 2 triangles and 1 rectangle. In this tutorial, we will discuss the formula for the area of a hexagon.

Hexagons

• A hexagon is a closed two-dimensional shape composed of six straight lines. It has six sides, six vertices, and six interior angles in two dimensions.

• A hexagonal floor tile, pencil cross-section, clock, honeycomb, and other real-world examples of the hexagon shape include: It can be regular (with six equal side lengths and angles) or irregular (with 6 unequal side lengths and angles).

• Regular Hexagon

  A regular hexagon is a closed 2D shape with six equal sides and six equal angles. Each regular hexagon angle measures 120 degrees.

  The total of all interior angles is 120 x 6 = 720 degrees. When it comes to exterior angles, we know that the sum of any polygon's exterior angles is always 360°. A hexagon has six exterior angles.

  As a result, each exterior angle in a regular hexagon measures $\mathrm{\frac{360}{6} = 60}$ degrees.

A regular hexagon differs from an irregular hexagon in that there is no definite measurement of angles and the lengths of sides differ. Some of the properties shared by irregular and regular hexagons are as follows −

• Both have six sides, six interior angles, and six vertices.

• All six interior angles add up to 720 degrees.

• All six exterior angles add up to 360 degrees.

Area of Hexagon

• The area of a hexagon is the region enclosed by the hexagon's sides.

  The area of a regular hexagon is $\mathrm{\frac{3\sqrt{3} s^2}{2}}$

  where s is the length of the hexagon's side. Because we're talking about a regular hexagon, all of the sides are the same length.

  When the length of one side of a regular hexagon is known, the area can be calculated using the formula

• The formula for calculating the area of a hexagon with a given apothem. Simply put, Area = $\mathrm{\frac{1}{2} × perimeter ×apothem}$.

Area of Hexagons by dividing into triangles

The side-side-side rule ensures that all triangles within the hexagon are congruent; each triangle has two sides inside the hexagon as well as a base side that forms the hexagon's perimeter. Similarly, all of the triangles have the same angles.

Hence the area of the hexagon will be given as ${\mathrm{6×\frac{\sqrt{3} s^2}{4}}}$

$$\mathrm{ =\frac{3\sqrt{3} s^2}{2}}$$

The area of a regular hexagon is $\mathrm{ \frac{3\sqrt{3} s^2}{2}}$ where s is the length of the hexagon's side.

Solved Examples

1) Find the area of the hexagon if the length of each side is 4.

Answer: It is given that the length of each side is 4 and we know that the area of a regular hexagon is $\mathrm{ \frac{3\sqrt{3} s^2}{2}}$ where s is the length of the hexagon's side.

The area of a regular hexagon=$\mathrm{ \frac{3\sqrt{3} s^2}{2}}$

$$\mathrm{ \frac{3\sqrt{3} \times 4^2}{2}}$$

$$\mathrm{=24\sqrt{3}}$$

2) Find the area of the hexagon if the length of each side is 2.

Answer: It is given that the length of each side is 2 and we know that the area of a regular hexagon is $\mathrm{ \frac{3\sqrt{3} s^2}{2}}$ where s is the length of the hexagon's side.

The area of a regular hexagon=$\mathrm{ \frac{3\sqrt{3} s^2}{2}}$

$$\mathrm{ \frac{3\sqrt{3} \times 2^2}{2}}$$

$$\mathrm{=6\sqrt{3}}$$

3) Find the area of the hexagon if its perimeter is 24 and apothem is 3.

We know the formula for calculating the area of a hexagon with a given apothem. Simply put,

$$\mathrm{Area =\frac{1}{2} × 24 ×3.}$$

$$\mathrm{=36}$$

4) Find the area of the hexagon if its perimeter is 4 and apothem is 1.

Answer: It is given that the perimeter is 4 and the apothem is 1.

We know the formula for calculating the area of a hexagon with a given apothem. Simply put,

$$\mathrm{Area =\frac{1}{2}× perimeter ×apothem.}$$

$$\mathrm{Area =\frac{1}{2}× 4 ×1.}$$

$$\mathrm{=2}$$

5) Find the perimeter of the hexagon whose area is 20 and apothem is 4.

Answer: It is given that the area of the hexagon is 20 and the apothem is 4.

Now use the relation, $\mathrm{Area =\frac{1}{2}× perimeter ×apothem.}$

$$\mathrm{20 =\frac{1}{2}\times perimeter \times 4}$$

$$\mathrm{\Rightarrow perimeter=10}$$

6) Find the perimeter of the hexagon whose area is 100 and apothem is 8.

Answer: It is given that the area of the hexagon is 100 and the apothem is 8.

Now use the relation, $\mathrm{Area =\frac{1}{2}× perimeter ×apothem.}$

$$\mathrm{100 =\frac{1}{2}× perimeter ×8.}$$

$$\mathrm{\Rightarrow perimeter=25}$$

7) Find the length of a regular hexagon if the given area is 6√3.

Answer: It is given that the area of the hexagon is 6√3.

Now use the relation the area of a regular hexagon=$\mathrm{\frac{3\sqrt{3} s^2}{2}}$

$$\mathrm{s=2}$$

8) Find the length of a regular hexagon if the given area is 3√3.

Answer: It is given that the area of the hexagon is 3√3.

Now use the relation the area of a regular hexagon=$\mathrm{\frac{3\sqrt{3} s^2}{2}}$

$$\mathrm{3\sqrt{3}=\frac{3\sqrt{3} s^2}{2}}$$

$$\mathrm{s=\sqrt{2}}$$

Conclusion

A hexagon is a six-sided polygon with six angles. It is derived from the Greek words "Hexa" for "six" and "gon" for "corner."

The area of a regular hexagon is $\mathrm{\frac{3\sqrt{3} s^2}{2}}$ where s is the length of the hexagon's side.

FAQs

1. What do you mean by hexagon?

A hexagon is a closed two-dimensional shape composed of six straight lines. It has six sides, six vertices, and six interior angles in two dimensions.

2. What is the formula for finding the area of a hexagon?

The formula for finding the area of the hexagon is $\mathrm{\frac{3\sqrt{3} s^2}{2}}$.

3. What are the Hexagon's Angles?

The sum of all six interior angles in a hexagon is 720 degrees. Each interior angle in a regular hexagon is 120 degrees.

4. What exactly is a regular hexagon?

A regular hexagon is a type of hexagon that has all of its sides equal. In addition, all six angles in a regular hexagon are equal.

5. What exactly is an Irregular Hexagon?

When compared to the other sides and angles, an irregular hexagon has at least one unequal side and angle. Each angle has no definite measurement, but the sum of all six interior angles is always 720 degrees, and the sum of all six exterior angles is 360 degrees.

6. How many symmetry lines are there in a regular hexagon?

The number of lines of symmetry for all regular polygons is equal to the number of sides. As a result, there are six lines of symmetry for a regular hexagon.