Question

If a hexagon of perimeter 24 cm has equal side lengths then the length of its side is _____.

Answer 1

Hint:
A hexagon is a polygon with six sides. In a regular hexagon all six sides and angles are equal. Use the formula of perimeter of hexagon= 6a where ‘a’ is the length of the side. Substitute the given value of perimeter in the formula and solve to get the value of a.

Complete step by step solution:
We will assume that this hexagon is a regular hexagon (all 6 sides have the same length)
The main characteristics of a regular hexagon has six equal sides and six equal angles.

Here the given perimeter of a regular hexagon is $24$cm. We have to find its side.
Perimeter is defined as the sum of all the sides of the polygon. Here we have been given a hexagon so the perimeter of a hexagon is the sum of the six sides of the hexagon.
We know that the formula for the perimeter of a regular hexagon is given as-
$$\Rightarrow Perimeterofhexagon=6a$$ where a is the length of the side.
On substituting given value of the perimeter of a hexagon in the formula we get,
$\Rightarrow 24=6\times a$
On simplifying we get,
$\Rightarrow a={\displaystyle \frac{24}{6}}=4$

Hence, the length of each side of a regular hexagon having perimeter 24 cm is 4 cm.

Note:
The properties of regular hexagon are-
It has six equal sides and six equal angles.
The total number of diagonals of a regular hexagon is nine.
The sum of interior angles of a regular hexagon is ${720}^{\circ }$ which means each interior angle is ${120}^{\circ }$ .
The sum of exterior angles of a regular hexagon is ${360}^{\circ }$ which means each exterior angle is ${60}^{\circ }$.
The formula for the area of hexagon=${\displaystyle \frac{3\sqrt{3}}{2}}\times a^2$ where ‘a’ is the length of the sides.