There are different types of hexagons, ranging from regular to irregular, and concave and convex hexagons.
The formula for the perimeter of a regular hexagon is given by,
P = 6a, where a is the length of one of its sides.
Here, each internal angle of the hexagon is 120°.
The perimeter formula for any other kind of hexagon other than a regular hexagon is given by,
P = Sum of all the six side lengths of a hexagon
Example 1: Calculate the perimeter of a regular hexagon with each side measuring 7 units.
Solution: Here, the side length, a = 7 units
As we have learned, the perimeter of a regular hexagon is given by,
P = 6a
P = 6 x 7
P = 42 units
Hence, the perimeter of the regular hexagon is 42 units.
Example 2: The perimeter of a hexagonal chessboard is 54 units. Find the side length of this chessboard.
Solution: The hexagonal chessboard has a perimeter of 54 units.
As we know, the formula for finding the perimeter of a hexagon is given by, P = 6a.
Here, we have to find the side length of the chessboard.
So, by substituting the values in the formula,
54 = 6a
We can write this as,
6a = 54
a = 54 ÷ 6
a = 9 units
Hence, each side of the hexagonal chessboard is 9 units in length.
Example 3: What is the perimeter of an irregular hexagon with sides 4 cm, 5 cm, 3 cm, 6 cm, 5 cm, 7 cm?
Solution: As we have learned, the perimeter formula for an irregular hexagon is the sum of its sides.
So, P = sum of the side lengths of a hexagon
P = 4 + 5 + 3 + 6 + 5 + 7
P = 30 cm
Hence, the perimeter of the irregular hexagon is 30 cm.
Example 4: Robert purchased a hexagonal prism that has an equal side length of 6 units. Find the perimeter of the hexagonal prism.
Solution: The hexagonal prism has six equal sides of 6 units. According to the perimeter of hexagon formula,
P = 6a
P = 6 x 6 [here a = 6 units]
P = 36 units
Hence, the hexagonal prism has a perimeter of 36 units.
The perimeter of a hexagon can be calculated by adding all its sides. The perimeter can be found by a simple formula as well, given by, P = 6a, where ‘a’ is the length of each side of a regular hexagon.
The sum of the interior angles of a hexagon is 720 degrees, where each interior angle is 120 degrees. In this case we are taking regular hexagons into consideration.
The perimeter formula for a rectangle is given by, P = 2 (l + w), where l is the length and w is the width of the rectangle.
The perimeter formula of a square is given by, P = 4a, where ‘a’ is the side length of the square.
The perimeter formula of a triangle is given by, P = a + b + c, where ‘a’ and ‘c’ are side lengths and ‘b’ is the base length of the triangle.