Area of a Hexagon
The area of a hexagon is the space that is enclosed by all its sides. Hexagon is a polygon with six angles and six sides. It is derived from the Greek words 'Hexa' which means 'six' and 'gonía' which means 'corner'. In this lesson, we will learn about the area of hexagon, the area of hexagon formula, and see how to find the area of a regular hexagon and the area of irregular hexagon.
| 1. | What is the Area of a Hexagon? |
| 2. | Area of 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 hexagon is the region that lies within the sides of the hexagon. A hexagon is a two-dimensional shape that has 6 sides, 6 angles, and, 9 diagonals, and the sum of its interior angles is 720°. The area of a hexagon can be calculated through various methods and it is expressed in square units, like m2, cm2, in2 or ft2, and so on.
Area of Hexagon Formula
The formula for the area of a regular hexagon is (3√3 s2)/2, where 's' is the length of the side of the hexagon. Since we are talking about a regular hexagon, it should be noted that all the sides are of equal length. When one side of the regular hexagon is known, the area can be calculated with the formula, Area of the hexagon = (3√3 s2)/2, where '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 can be calculated when the side length is given. The formula that is used in this case is, Area of regular hexagon = (3√3 s2)/2. Thus, we follow the steps given below to find the area of hexagon:
Area of Regular Hexagon
Let us see how to find the area of a regular hexagon.
- Step 1: Identify the length of the side of the regular hexagon.
- Step 2: Find the area using the formula for area of a regular hexagon, Area of hexagon = (3√3 s2)/2; where 's' is the side length.
- Step 3: Represent the final answer in square units.
Example: Find the area of a regular hexagon that has a side length of 6 inches.
Solution: Given the length of the side = 6 inches. Let use the formula for area of a regular hexagon
Area of Hexagon = (3√3 s2)/2 = (3 × √3 × 62)/2 = 54√3 = 93.5 in2
Answer: The area of the regular hexagon is 93.5 in2.
Area of Hexagon with Apothem
The area of a regular hexagon can be calculated when the side length and the apothem is given. Apothem is the line segment that is drawn from the center and is perpendicular to the side of the hexagon. Observe the following hexagon to see the apothem and the formula to find the area of a regular hexagon when the apothem is given.
The formula that is used in this case is, Area of hexagon = (1/2) × apothem × Perimeter of hexagon, or, Area of hexagon = (1/2) × a × P = (1/2) × a × 6 × s = 3as,
- where 'a' is the length of an apothem
- P is the perimeter of the hexagon
- 's' is the length of the side of the hexagon
Let us understand this with the help of an example.
Example: Find the area of a hexagon in which the apothem is 12 units and the side length is 8√3 units.
Solution: The area of the hexagon can be calculated using the formula: Area of hexagon = (1/2) × apothem × Perimeter of hexagon
We know that the apothem = 12 units, perimeter of hexagon = 6 × 8√3 units = 48√3 units
So, after substituting the values in the formula, we get, Area of hexagon = (1/2) × 12 × 48√3 = 288√3 = 498.8 square units.
Area of Irregular Hexagon
The area of an irregular hexagon does not have any specific formula. An irregular hexagon can be divided into different shapes like rectangles and triangles. After this, the area of these shapes can be calculated and added together to get the area of the hexagon.
Area of Hexagon Calculator
The area of a hexagon can be calculated using the formulas given above. And the answers can be verified using Cuemath's online Area of Hexagon Calculator, which calculates the area within minutes once the given parameters are entered.
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FAQs on Area of a Hexagon
What is the Area of Hexagon?
The area of the hexagon is defined as the area enclosed within the sides of the hexagon. The area of a hexagon is expressed in square units like m2, cm2, in2, ft2, and so on.
What is the Formula for Area of a Hexagon?
The formula for the area of a hexagon is Area = (3√3 s2)/2; where 's' is the length of one side of the regular hexagon. The formula for the area of a hexagon can also be given in terms of the apothem as, Area of hexagon = (1/2) × a × P; where 'a' is the length of the apothem and 'P' is the perimeter of the hexagon.
How to Find the Area of a Hexagon?
We can find the area of a regular hexagon using the following steps. Let us find the area of a hexagon with side length of 8 units.
- Step 1: Identify the length of the side of the hexagon. Here, the side length (s) = 8 units.
- Step 2: Find the area of a hexagon using the formula, A = (3√3 s2)/2 to get the final answer in square units. Substituting the values in the formula, A = (3√3 s2)/2 = (3√3 × 82)/2 = 96√3 = 166.28 square units.
How to Find the Area of Hexagon with Apothem?
Apothem is the line segment that is drawn from the center and is perpendicular to the side of the hexagon. We can find the area of a regular hexagon with apothem using the formula, Area of hexagon = (1/2) × a × P; where 'a' is the apothem and 'P' is the perimeter of the hexagon.
What is the Formula for Perimeter and Area of a Hexagon?
The formula that is used to calculate the area of a regular hexagon is (3√3 s2)/2; where 's' is the side length. The perimeter of a hexagon can be calculated by adding all six side lengths. In the case of a regular hexagon, we use the formula, Perimeter = 6 × s; where 's' is the length of one side.
How to Find the Area of Irregular Hexagon?
There is no specific formula to find the area of an irregular hexagon. The hexagon can be divided into different shapes like rectangles and triangles. After this, the area of these shapes can be calculated and added together to get the area of the hexagon.
How to Find Area of Hexagon Inscribed in a Circle?
In order to find the area of a regular hexagon inscribed in a circle, we can first divide the hexagon into 6 triangles which will be equilateral triangles. Now, since the hexagon is inscribed in a circle, the radius of the circle will be the side of the triangle. We know that the area of an equilateral triangle is calculated with the formula, area of equilateral triangle = √3/4 × side2. So, the area of hexagon will be 6 times this area because the hexagon is divided into 6 equilateral triangles. Therefore, the formula to find the area of hexagon inscribed in a circle = 6 × √3/4 × side2. Here, the radius will be considered as the side length.
What is the Area of Hexagon with Side Length 6 units?
If the side length of a regular hexagon is 6 units, the area can be calculated with the formula, Area of hexagon = (3√3 s2)/2; where 's' is the side length. On substituting the value of s = 6 in the formula, Area of hexagon = (3√3 × 62)/2 = (3√3 × 36)/2 = 93.53 square units.
What is the Area of Regular Hexagon Formula?
The formula for the area of a regular hexagon is Area = (3√3 s2)/2; where 's' is the side length. This means if we know the side length of a regular hexagon, we can easily find the area using this formula.
How to find the Apothem of a Hexagon?
The apothem of a hexagon can be calculated if the area of the regular hexagon is known. We can use the formula, Area of hexagon = (1/2) × a × P; where 'a' is the apothem and 'P' is the perimeter of the hexagon. In this formula, we can substitute the given values and find the unknown value of the apothem. For example, let us find the apothem of a regular hexagon whose area is 36 square units.
- Step 1: We know that the area of the regular hexagon is 36 unit2. So, we can find the side length using the formula, Area = (3√3 s2)/2. After substituting the value of Area as 36, we get, 36 = (3√3 s2)/2. This gives us the value of side length as, 3.72 units
- Step 2: Now, that we know the side length which is 3.72 units, we can find the perimeter of the hexagon which will be 3.72 × 6 = 22.32 units.
- Step 3: Now, let us find the apothem using the formula, Area of hexagon = (1/2) × a × P, in which we know the area and the perimeter. So, after substituting the given values, we get, Area of hexagon = (1/2) × a × P. This will be 36 = (1/2) × a × 22.32. So, the value of the apothem 'a' will be, 3.22 units