Diagonal of Hexagon
The diagonals of a hexagon are drawn by joining any two non-adjacent vertices of a hexagon. A total of 9 diagonals can be formed in a hexagon. Let us learn more about the diagonals of a hexagon on this page.
| 1. | What is the Diagonal of a Hexagon? |
| 2. | Number of Diagonals in a Hexagon |
| 3. | Regular Hexagon Diagonals |
| 4. | Diagonal of a Hexagon Formula |
| 5. | FAQs on Diagonal of Hexagon |
What is the Diagonal of a Hexagon?
The diagonal of a hexagon is the line segment that connects the non-adjacent vertices. One single vertex can form 3 diagonals and there are 6 vertices in a hexagon. Observe the figure given below to see the diagonals of a hexagon.
Number of Diagonals in Hexagon
There are 9 diagonals in a hexagon. If we take any 3 consecutive vertices in a hexagon and start connecting them to the other non-adjacent vertices, we will get 9 diagonals in all. For example, in the figure given above, let us take the vertices D, E and F and join them to the other vertices that are non-adjacent to them. This will form the diagonals in the following way.
- Diagonals from Vertex D: DF, DA, DB
- Diagonals from Vertex E: EA, EB, EC
- Diagonals from Vertex F: FB, FC
- Diagonal joining Vertex A and C: AC
Regular Hexagon Diagonals
A regular hexagon is one in which all the sides are of equal length and all the interior angles are of equal measure. This means that each interior angle of a regular hexagon is equal to 120°. Now, the number of diagonals that can be drawn in a regular hexagon is 9. These can be formed by joining the non-adjacent vertices as shown in the figure given above.
Diagonal of a Hexagon Formula
The number of diagonals that can be formed in a polygon can be calculated using the formula, Number of diagonals in a polygon = 1/2 × n × (n-3), where n = number of sides in the polygon. Here, n = 6. After substituting this value of n = 6 in the formula we get, Number of diagonals in a polygon: 1/2 × n × (n-3) = 1/2 × 6 × (6 - 3) = 9. Therefore, 9 diagonals can be drawn in a hexagon.
Length of Diagonal of Hexagon with Side Length
The length of the diagonal of a hexagon can be calculated if the side length of the regular hexagon is given. We know that 6 equilateral triangles can be formed inside a regular hexagon. This fact helps to find the length of the diagonal of the hexagon when we know one side of the regular hexagon.
Example: Find the length of the diagonal of a hexagon if the side length of the regular hexagon is 3 cm.
Solution: Since it is a regular hexagon, we know that 6 equilateral triangles can be formed inside it. This means the length of the diagonal can be calculated if the side length of the regular hexagon is known. Observe the figure given below to see the regular hexagon with 6 equilateral triangles.
This means the diagonal will be twice the length of the side of the hexagon. Here, the length of side = 3 cm, so the length of the diagonal of a regular hexagon = 2 × side length = 2 × 3 = 6 cm
Therefore, the length of the diagonal of the hexagon is 6 cm.
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FAQs on Diagonal of a Hexagon
What are the Diagonals of a Hexagon?
The line segments that connect the non-adjacent vertices of a hexagon are known as the diagonals of a hexagon. A total of 9 diagonals can be formed in a hexagon.
What is the Diagonal of a Hexagon Formula?
The formula for finding the number of diagonals in a hexagon is, Number of diagonals in a polygon = 1/2 × n × (n-3), where n = number of sides in the polygon. Here, n = 6. After substituting this value of n = 6 in the formula we get, Number of diagonals in a polygon: 1/2 × n × (n-3) = 1/2 × 6 × (6 - 3) = 9. Therefore, 9 diagonals can be drawn in a hexagon.
What is the Maximum Number of Distinct Diagonals in a Hexagon?
The maximum number of distinct diagonals that can be formed in a hexagon are 9. These are drawn by connecting the non-adjacent vertices.
How to Find the Number of Diagonals in a Hexagon?
In order to find the number of diagonals of a hexagon the following methods can be used.
- Number of diagonals in a polygon = 1/2 × n × (n-3), where n = number of sides in the polygon. Here, n = 6. After substituting this value of n = 6 in the formula we get, Number of diagonals in a polygon: 1/2 × n × (n-3) = 1/2 × 6 × (6 - 3) = 9. Therefore, 9 diagonals can be drawn in a hexagon.
- Take any 3 vertices and connect them to the other non-adjacent vertices without repetition and join any remaining vertices that are left. This will also result in 9 diagonals.
How to Find the Length of the Diagonal of a Regular Hexagon?
A regular hexagon is one in which all the sides are of equal length and 6 equilateral triangles can be formed inside it. This means the length of the diagonal can be calculated if the side length of the regular hexagon is known. For example, if the side length of a regular hexagon is 7 cm, let us find the length of the longest diagonal of the hexagon. In this case, we know that 6 equilateral triangles can be formed inside a regular hexagon, this means the diagonal will be twice the length of the side of the hexagon. Here, the length of side = 7 cm, so the length of the diagonal = 2 × 7 = 14 cm.
How to Find the Diagonal of a Hexagon when the Perimeter is Given?
The length of the diagonal of a regular hexagon can be calculated when its perimeter is given. For example, if the perimeter of a regular hexagon is 48 cm, let us find the length of its diagonal using the following steps.
- Step 1: Since it is a regular hexagon and we know the perimeter, the length of one side can be calculated with the formula, Perimeter of a regular hexagon = 6 × side.
- Step 2: After substituting the values in the formula, we get, Perimeter of a regular hexagon = 6 × side. 48 = 6 × side. So, side = 48/6 = 8 cm.
- Step 3: Now, that the side length is known, the diagonal length can be calculated because we know that 6 equilateral triangles can be formed inside a regular hexagon, this means the diagonal will be twice the length of the side of the hexagon. Here, the length of side = 8 cm, so the length of the diagonal = 2 × 8 = 16 cm.
What is the Length of the Diagonal of a Hexagon with Side Length 4 units?
If the side length of a regular hexagon is given, then the length of the diagonal can be calculated. It is to be noted that 6 equilateral triangles can be formed inside a regular hexagon. This means that the length of the diagonal will be twice the length of the side of the hexagon. In this case, the length of side = 4 units, so the length of the diagonal = 2 × 4 = 8 units. Therefore, the length of the diagonal of the hexagon is 8 units.