Area of a Hexagon
The area of a hexagon is the area that is enclosed by all six (Hexa) sides of the hexagon along with solved examples. The word hexagon is derived from the Greek words "Hexa" which means "six" and "gonía" which means "corner". In this lesson, we will learn about the formula of the area of a hexagon and determine the area of a hexagon. Stay tuned to learn more about the area of a hexagon!!!
1.  What is Area of a Hexagon? 
2.  Area of a Hexagon Formula 
3.  How to Find the Area of a Hexagon? 
4.  FAQs on Area of a Hexagon 
What Is the Area of a Hexagon?
The area of the hexagon is the area that is within the sides of the hexagon. A hexagon is a polygon having six sides. A hexagon has 9 diagonals, and the sum of its interior angles of the hexagon equals 720°. As a hexagon is a twodimensional shape, thus the area of the hexagon also lies in a twodimensional plane. The unit of area of a hexagon is given in square units, m^{2}, cm^{2}, in^{2} or ft^{2}, etc.
Area of a Hexagon Formula
The formula for the area of the hexagon is (3√3 S^{2})/2 where s is the length of the side of the hexagon. To calculate the area of the hexagon we can use the area of an isosceles triangle. We divide the area of the hexagon into 6 isosceles triangles and calculate it accordingly.
Area of the hexagon = (3√3 S^{2})/2 where S is the length of the side of the hexagon. We can also find the area of a hexagon in terms of apothem. Apothem is the line segment drawn perpendicular to the side of the hexagon from the center of the hexagon. Area of a regular hexagon with a length of the side and an apothem of length given, A = (1/2)aP = (1/2) × a × 6 × S = 3aS where a is the length of an apothem, P is the perimeter of the hexagon and S is the length of the side of the hexagon
How to Find the Area of a Hexagon?
As we learned in the previous section, the area of a hexagon is (3√3 S^{2})/2. Thus, we follow the steps shown below to find the area of the hexagon.
 Step 1: Identify the length of the side of the hexagon and name it to be S.
 Step 2: Find the area of a hexagon using the formula = (3√3 S^{2})/2.
 Step 3: Represent the final answer in square units.
Example: Find the area of a regular hexagon having the length of the side 6 inches.
Solution: Given the length of side = 6 inches
Area of a Regular Hexagon = (3√3 S^{2})/2 = (3√3 6^{2})/2 = 54√3 in^{2}
Answer: The area of the regular hexagon is 54√3 in^{2}
Solved Examples on Area of a Hexagon

Example 1: Find the area of a regular hexagon having a side of length 10 units.
Solution: Given the length of side = 10 units
Area of a Regular Hexagon = (3√3 S^{2})/2 = (3√3 10^{2})/2 = 150√3 units^{2}Answer: Area of the regular hexagon = 150√3 units^{2}

Example 2: Find the length of the side of the hexagon given its area = 600√3 units^{2}.
Solution: Given that area of a hexagon= 600√3 units^{2}
Thus, (3√3 S^{2})/2 = 200√3
⇒ S^{2} = 400
⇒ S = 20 unitsAnswer: Thus, the length of a side of the regular hexagon is 20 units
FAQs on the Area of a Hexagon
What is the Area of a Hexagon?
The area of the hexagon is defined as the area enclosed within the sides of the hexagon. The area of a hexagon is given in square units like m^{2}, cm^{2}, in^{2} or ft^{2}, etc.
What is the Formula for Area of a Hexagon?
The formula for the area of a hexagon is given as A = (3√3 S^{2})/2 S is the length of the side of the hexagon. The formula of the area of a hexagon can also be given in terms of apothem as A = (1/2)aP where a is the length of an apothem and P is the perimeter of the hexagon.
How to Find Area of a Hexagon?
We can find the area of a hexagon using the following steps:
 Step 1: Identify the length of the side of the hexagon.
 Step 2: Find the area of a hexagon using the formula, A = (3√3 S^{2})/2.
 Step 3: Write the final answer obtained in square units.
How to Find Area of a Regular Hexagon with an Apothem?
We can find the area of a regular hexagon with apothem using the following steps:
 Step 1: Identify the given dimensions of the hexagon.
 Step 2: Find the area of a hexagon using the formula, A = (1/2)aP
 Step 3: Write the final answer obtained in square units.
What Happens to the Area of a Hexagon If the Length of Side is Doubled?
The area of the hexagon is quadrupled if the length of the side of the hexagon is doubled as "S" gets substituted by "2S" in the formula of area, A = (3√3 S^{2})/2 = (3√3 (2S)^{2})/2 = 4(3√3 S^{2})/2 which gives four times the original value of the area of the hexagon.
What Happens to the Area of a Hexagon If the Length of Side is Halved?
The area of the hexagon becomes one fourth if the length of the side of the hexagon is halved as "S" gets substituted by "S/2" in the formula of area, A = (3√3 S^{2})/2 = (3√3 (S/2)^{2})/2 = (1/4)×(3√3 S^{2})/2 which gives one fourth the original value of the area of the hexagon.