# Area of a Regular Hexagon

🏆Practice regular hexagon

## Calculation of the Area of a Regular Hexagon - Let's Calculate It This Way!

The regular hexagon belongs to the family of regular polygons. It is a polygon in which all sides, and all angles, are equal to each other. By its name, we can understand that it is a geometric figure with $6$ different sides. The sum of its internal angles equals $720^o$ degrees. Therefore:

external angle $=60^o$ ; internal angle $=120^o$

## Test yourself on regular hexagon!

Given the hexagon in the drawing:

What is the area?

Three diagonals divide the regular hexagon into six congruent isosceles triangles. Therefore, the calculation of the area of a hexagon, whose side is a:

$6\times\frac{a^2\sqrt{3}}{4}$

Assuming that the length of the side of the regular hexagon is $4$ cm, its area will be:

#### $6\frac{a^2\sqrt{3}}{4}=41.57$

How many sides does a regular hexagon have?

The hexagon is a geometric figure with 6 equal sides

## Exercises with Hexagons

### Exercise 1

Given a regular hexagon

with a perimeter of $72$ cm

Calculate the area of the hexagon

Calculate the area of the hexagon

Solution

Since the hexagon has 6 equal sides we will divide $72$ by $6$

$\frac{72}{6}=12$

Each side is equal to $12$ cm

And then we will place the side in the formula to find the area of the hexagon

$A=6\cdot\frac{(12)^2\cdot\sqrt{3}}{4}=374.12$

The correct answer is $374.12$ cm²

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### Exercise 2

Given that the area of the hexagon is equal to $6$ cm²

What is the value of the sides of the hexagon?

Solution

We place the side of the hexagon as $X$ in the formula

Given that the area is equal to $6$ cm²

$A=\frac{6\cdot(X)^2\cdot\sqrt{3}}{4}$

Multiply by 4

$24=6\cdot X^2\cdot\sqrt{3}~~~~$

Now divide by 6

$4= X^2\cdot\sqrt{3}$

Divide by $~~~~\sqrt{3}$

$X^2=\frac{4}{\sqrt{3}}$

$X=1.526$ cm

$X=1.526$ cm

### Exercise 3

Given the regular hexagon with an area of $(\sqrt{3})^3$

Calculate the value of the sides of the hexagon

Solution

We use the formula to find the area of the hexagon:

Given that $A=(\sqrt{3})^3$ we represent the side as $X$.

Area of the hexagon =

$A=(\sqrt{3})^3$

We represent the side with $X$.

$A=6\cdot\frac{(X)^2\cdot\sqrt{3}}{4}=(\sqrt{3})^3$

We multiply both sides by $4$

$4\cdot(\sqrt{3})^3=6\cdot X^2\cdot\sqrt{3} ~~~~~$

We divide by $:√3$

$4\cdot(\sqrt{3})^2=6\cdot X^2$

$4\cdot3=6X^2 ~~~~~~$

Now we divide by $:6$

$2=X^2$

$X=\sqrt{2}$

The answer is $X=\sqrt{2}$

Do you know what the answer is?

### Exercise 4

Regular hexagon with an area of $12$ cm².

How much is each side of the hexagon worth?

Solution

We place on the side $X$ the formula

(Given: the area of the hexagon is $12$ cm²)

$A=6\cdot\frac{(X)^2\cdot\sqrt{3}}{4}=\frac{12}{1}$

We multiply the whole expression by 4

$6X^2\cdot\sqrt{3}=12\cdot4~~~~~$

We divide by $:6$

$X^2\cdot\sqrt{3}=8$

We divide by $\sqrt{3}$

$X^2=\frac{8}{\sqrt{3}}$

$X=\sqrt{\frac{8}{\sqrt{3}}}=2.149$

The side of the hexagon is worth $2.149$ cm.

### Exercise 5

Given that the area of the regular hexagon is equal to $8$ cm²

Calculate the value of the sides of the hexagon.

Solution

We place in the formula to find the area of the hexagon: $A=8$ and we will represent the side as $X$

$A=6\cdot\frac{(X^2)\sqrt{3}}{4}=\frac{8}{1}$

Multiply by $4$

$8\cdot4=6\cdot X^2\sqrt{3}=\frac{8}{1}$

$32=6\sqrt{3}\cdot X^2 ~~~~~~$

Divide the expression by $:6\sqrt{3}$

$X^2=3.07$

$X^=\sqrt{3.07}$

The correct answer is $X^=\sqrt{3.07}$

### Exercise 6

Given that the area of the regular hexagon has a value of $49$ cm²

Calculate the value of the sides of the hexagon.

Solution

We place in the formula to find the area of the hexagon $A=49$ cm² and the side will be represented as $X$.

$A=6\cdot\frac{X^{2\cdot}\sqrt{3}}{4}=\frac{49}{1}$

Multiply by $4$

$6\sqrt{3}X^2=4\cdot49~~~~~$

Divide by $:6\sqrt{3}$

$X^2=18.86$

Finally, we take the square root $√$

$X=4.34$

$X=4.34$

## Take private lessons online, from the comfort of your home!

Calculating the area of a regular hexagon can only be done if we understand its shape and properties. If you feel that you do not understand your teacher's explanations in the classroom, you can get in touch with one of our private tutors. Even if what you need is to complete part of the material that you have not understood in the classroom, an online private tutor can help you with just a few classes, in which you can study exactly what you are missing.

You can also coordinate an online private math class, right from your personal computer! How do you have an online private class?

• First, you will have a small talk with the teacher.
• Explain to the teacher what topic you want to study.
• Discuss what difficulties you have in your studies.
• The teacher will explain what you do not understand.
• Practice during the class, the material you are studying. For example, calculating the area of a regular hexagon.

Do you think you will be able to solve it?

Well, as you should already know, the more you practice, the better you will understand. First, when you start to apply a new formula, many doubts usually arise. After having done about 5 exercises, you will feel that you are beginning to better understand the new geometric shape you are studying, and the calculation of its area. Therefore, what we recommend is that you practice as much as possible. What do you achieve by exercising?

• It is not necessary to start by memorizing the formula, but you will gradually remember it as you use it.
• When you study regular hexagons, you will come across a variety of exercises, which include different data.
• Each exercise you do will help you become familiar with this geometric shape.
• Gradually, it will take you less time to solve the different problems.
• And you will feel more confident about yourself.

## "What suits me best, a private lesson just for you, or together with a study partner?"

A private class along with another classmate is only recommended in cases where both are interested in studying the same topics. Since when you have a private class, it is more than important to use the time effectively. The ultimate goal is for you to understand the material being taught. If two students take a class together, and both are interested in different topics, surely the class cannot be taken full advantage of.

## Study math throughout the year, and not just before exams.

Mathematics is a subject whose topics are learned gradually. Almost any formula, topic, or model you learn will also apply to the following topics. Therefore, it is important to avoid falling behind. If you feel that you need to reinforce a specific topic, get in touch with one of our teachers. The best way to learn mathematics is by dedicating time and study throughout the year, and not by cramming right before each exam. Good luck!

Do you know what the answer is?

## examples with solutions for regular hexagon

### Exercise #1

Given the hexagon in the drawing:

What is the area?

64.95

### Exercise #2

Given the hexagon in the drawing:

What is the area?

166.27

### Exercise #3

Given the hexagon in the drawing:

What is the area?

41.56

### Exercise #4

A hexagon has an area of 8 cm².

How long are the sides of the hexagon?

### Video Solution

$\sqrt{3}$ cm

### Exercise #5

A hexagon has sides
measuring 6 cm long.

What is the area of the hexagon?