Question

Four regular hexagons are drawn so as to form the design as shown. If the perimeter of the design is $28{\text{ cm}}$. Find the length of each side of the hexagon.

Answer 1

Hint:
Assume the length of each side of the design to be a cm as a regular hexagon has an equal number of sides. Now count the number of sides of the design. Then use the formula-
The perimeter of regular hexagon = number of sides × length of the side
Now put the values of perimeter and number of sides in the formula and solve the obtained function to get the answer.

Complete step by step solution:
Given, four regular hexagons are drawn as shown below-

The perimeter of the design=$28{\text{ cm}}$
We have to find the length of each side of the hexagon.
A regular hexagon has equal sides and equal angles. So, all the sides of the given design have equal sides. Let the length of one side is a cm.
According to the arrangement of hexagons, the number of sides=$14$
Now we know that perimeter is the sum of all sides of the polygon.
So we can write, the perimeter of given regular hexagon = number of sides × length of the side
On putting the values of perimeter, length, and number of sides we get-
$ \Rightarrow 28 = 14 \times a$
On adjusting, we get-
$ \Rightarrow a = \dfrac{{28}}{{14}}$
On division, we get-
$ \Rightarrow a = 2$

Hence the length of each side of the hexagon is $2{\text{ cm}}$.

Note:
The properties of a regular hexagon are-
1) It has six sides and six angles.
2) All the sides and measures of angles are equal to each other.
3) The regular hexagon has total $9$ diagonals.
4) The sum of all the interior angles of a regular hexagon is ${720^ \circ }$ and each interior angle is equal to ${120^\circ }$.
5) The sum of all exterior angles of a regular hexagon is ${360^\circ }$ and each exterior angle is equal to ${60^\circ }$.