One of the most important reasons why we are intimidated when it comes to geometry is that there are geometric shapes that we do not see around us, such as hexagons. Since we don’t see many examples of these shapes in our daily life, when we open a geometry book or see the question of how to find the area of a hexagon, it inevitably causes us to get nervous and create question marks in our minds.
Do not worry, there is an answer to the question of how to calculate the area of the hexagon, but not as we know it. Because the hexagon, as its name suggests, is a somewhat complex shape, there are different methods to be applied in special cases and special formulas to be used in these methods. Let’s take a closer look at how the area of the hexagon is calculated in its simplest form and see the methods you can apply.
First of all, let’s get to know our shape; What is a hexagon?
Polygons with six sides and six corners are called hexagons. Hexagons with equal sides and interior angles are called regular hexagons. The interior angles of a regular hexagon made up of six equilateral triangles are each 120 degrees, and the sum of the interior angles is 720 degrees. Each exterior angle is 60 degrees.
Briefly, the main features of the hexagon:
- A hexagon has six sides.
- A hexagon has six corners.
- An interior angle of a hexagon is 120 degrees.
- The sum of the interior angles of a hexagon is 720 degrees.
- An exterior angle of a hexagon is 60 degrees.
- The sum of the exterior angles of a hexagon is 360 degrees.
- A hexagon has nine diagonals.
- The perimeter of a hexagon is found by adding the perimeter of the sides.
- A hexagon is formed by joining six equilateral triangles.
How to find the area of a hexagon? Here are the methods you can apply in different ways:
- Method #1: Calculating the area of a regular hexagon based on its side length
- Method #2: Calculating the area of a regular hexagon based on its inner radius
- Method #3: Calculating the area of an irregular hexagon with respect to its vertices
Method #1: Calculating the area of a regular hexagon based on its side length:
- Step #1: The area formula of the hexagon is Area = ( 3√3 x s² )/2.
- Step #2: The side length of the regular hexagon is denoted as s.
- Step #3: Let’s find the side length of the hexagon as perimeter / 6.
- Step #4: Let’s say 54 / 6 = 9
- Step #5: A side length can also be found with a = x√3 x 2 if you know the inner radius.
- Step #6: Substitute the side length of 9 cm in the formula Area = ( 3√3 x 9² ) / 2
- Step #7: Area = ( 3√3 x 81 ) / 2
- Step #8: Area = ( 243√3 ) / 2
- Step #9: Area = 420.8 / 2
- Step #10: Area = 210.4
- Step #11: The area is shown in square meters so Area = 210.4 cm²
To calculate the area of a regular hexagon based on its side length, simply follow the steps above. The steps may vary depending on the shape of the hexagon, but if you are going to do a basic operation, the formula and steps will be the same or similar.
Method #2: Calculating the area of a regular hexagon based on its inner radius:
- Step #1: In this figure, the area formula for the hexagon is Area = 1/2 x perimeter x inner radius.
- Step #2: Let’s say the inner radius of the hexagon is 5√3 cm.
- Step #3: Let’s say the side length is 10 cm.
- Step #4: 10 x 6 = 60 cm is the perimeter of the hexagon.
- Step #5: Let’s put the data in the formula Area = 1/2 x 60 x 5√3
- Step #6: Area = 30 x 5√3
- Step #7: Area = 150√3
- Step #8: Area = 259.8
- Step #9: The area is shown in square meters so Area = 259.8 cm²
To calculate the area of a regular hexagon based on its inner radius, simply follow the steps above. The steps may vary depending on the shape of the hexagon, but if you are going to do a basic operation, the formula and steps will be the same or similar.
Method #3: Calculating the area of an irregular hexagon based on its vertices:
- Step #1: First, let’s make a list of hexagon vertices, 7 rows and x and y columns.
- Step #2: Let’s say;
- A: (4, 10)
- B: (9, 7)
- A: (11, 2)
- D: (2, 2)
- E: (1, 5)
- F: (4, 7)
- A: (4, 10) yes it is rewritten.
- Step #3: Multiply the vertices in the x and y shape diagonally;
- 4 x 7 = 28
- 9 x 2 = 18
- 11 x 2 = 22
- 2 x 5 = 10
- 1 x 7 = 7
- Step #4: Let’s sum the results 28 + 18 + 22 + 10 + 7 + 40 = 125
- Step #5: Multiply the corner points diagonally by y and x;
- 10 x 9 = 90
- 7 x 11 = 77
- 2 x 2 = 4
- 2 x 1 = 2
- 5 x 4 = 20
- 7 x 4 = 28
- Step #6: Let’s sum the results 90 + 77 + 4 + 2 + 20 + 28 = 221
- Step #7: Subtract the second result from the first so 125 – 221 = -96
- Step #8: Since the area must be positive, let’s divide the result in two, i.e. 96/2 = 48
- Step #9: The area is shown in square meters so Area = 48 m²
To calculate the area of an irregular hexagon with respect to its vertices, simply follow the steps above. The steps may vary depending on the shape of the hexagon, but if you are going to do a basic operation, the formula and steps will be the same or similar.
We shared different methods that you can apply by answering the question of how to find the area of the hexagon, which is one of the most confusing topics in geometry. There may be changes in the method steps depending on the process you will do.
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