how to find the area of a hexagon
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 and the formula used to find the area of a hexagon.
| 1. | What is the 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 hexagon is the region that lies within the sides of the hexagon. A hexagon is a two-dimensional shape that has 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 a 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.
- Step 1: Identify the length of the side of the regular hexagon.
- Step 2: Find the area using the formula, Area of hexagon = (3√3 s2)/2; where 's' is the side length and represents 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 side = 6 inches
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 of the hexagon 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 and
- 's' is the length of the side of the hexagon.
Related Links:
- Hexagon
- Area of Polygons
Solved Examples on Area of a Hexagon
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Example 1: Find the area of a regular hexagon that has a side length of 10 units.
Solution: Given the length of side = 10 units
Area of a Regular Hexagon = (3√3 s2)/2 = (3 × √3 × 102)/2 = 150√3 = 259.8 units2Answer: Area of hexagon = 259.8 units2
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Example 2: Find the side length of a regular hexagon which has an area of 600√3 units2.
Solution: Given, area of a hexagon = 600√3 units2; formula to find the area of a hexagon = (3√3 s2)/2
Therefore, the side length can be calculated using this formula when the area is known. (3√3 s2)/2 = 600√3
(3√3 s2) = 600√3 × 2
⇒ s2 = (600√3 × 2)/3√3
⇒ s2 = 400
⇒ s = 20 unitsAnswer: Thus, the length of the side of the regular hexagon is 20 units.
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Practice Questions on Area of a Hexagon
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FAQs on the 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 7 units.
- Step 1: Identify the length of the side of the hexagon. Here, the side length (s) = 7 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 = 166.27 square units.
How to Find the Area of Hexagon with Apothem?
Apothem is the line segment that is drawn from the center of the hexagon 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 Area and Perimeter of a Hexagon?
The formula that is used to calculate the area of a regular hexagon is, Area of hexagon = (3√3 s2)/2; where 's' is the side length of the hexagon. The perimeter of a hexagon can be calculated by adding all the six side lengths. In 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 accordingly. 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.
how to find the area of a hexagon
Source: https://www.cuemath.com/measurement/area-of-a-hexagon/
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