Question

If the area of a regular hexagon is $24\sqrt 3 $ sq.cm. Find its side.

Answer 1

Hint: A hexagon is polygon with six sides. In a regular hexagon all six sides and angles are equal. Use the formula of area of hexagon=$\dfrac{{3\sqrt 3 }}{2} \times {a^2}$ where ‘a’ is the length of the side. Put the given values in the formula and solve to get the answer.

Complete step-by-step answer:
A regular hexagon has equal sides and equal angles.

Here the given area of a regular hexagon is $24\sqrt 3 $sq.cm. We have to find its side.
We know that the formula for the area of hexagon is given as-
$ \Rightarrow $ Area of hexagon=$\dfrac{{3\sqrt 3 }}{2} \times {a^2}$ where a is the length of the side.
On putting given values in the formula we get,
$ \Rightarrow 24\sqrt 3 = \dfrac{{3\sqrt 3 }}{2} \times {a^2}$
On simplifying we get,
$ \Rightarrow 24 = \dfrac{3}{2} \times {a^2}$
On finding the value of ‘a’ we get,
$ \Rightarrow {a^2} = \dfrac{{24 \times 2}}{3}$
On solving further we get,
$ \Rightarrow {a^2} = 8 \times 2 = 16$
On removing square from ‘a’ we get,
$ \Rightarrow a = \sqrt {16} = 4$
Hence, the length of each side of a regular hexagon having area $24\sqrt 3 $sq.cm. is $4$ cm.

Note: The properties of regular hexagon are-
It has six sides and six angles and all of them are equal.
The total number of diagonals of a regular hexagon is$9$ .
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 perimeter of hexagon=$6a$ where ‘a’ is the length of the sides.