Question

Find the number of diagonals of a hexagon.

Answer 1

In this question, we have to find out the number of diagonals of hexagon. Hexagon is a three dimensional geometrical figure having six sides and diagonal is nothing but connects two non-consecutive vertices of any Polygon and here is hexagon. Non-Consecutive vertices means those vertices which are not attached to each other means not continuous.

Complete answer:
In the question, we have to find out the number of diagonals of a hexagon. For calculating the number of diagonals, first of all we should know about the number of sides of a hexagon. A hexagon is a six sided closed three dimensional geometrical figure. It means hexagon is having $6$ vertices. For finding the number of diagonals of a regular polygon, we have the formula for finding it and the formula is number of diagonals $= n\dfrac{{\left( {n - 3} \right)}}{2}$
Where $x$is the number of sides or number of vertices of a regular polygon and Here the given polygon is hexagon.
And for hexagon, number of sides $= 6$
Therefore the formula for finding the diagonals of a hexagonal can be calculated by substituting
$n = 6$ sides of a hexagon.
Therefore, We get number of diagonals $= 6\dfrac{{\left( {6 - 3} \right)}}{2}$
Where $\left( {6 - 3} \right)$ gives $3$
So, number of diagonal $= \dfrac{{6 \times 3}}{2}$
Where $6 \times 3$ gives $18$ , And we get $\dfrac{{18}}{2}$ , Which implies \dfrac{{18}}{2}$$$$ = 9

Therefore, the number of diagonals of a regular hexagon is $9$. Where diagonal is non-consecutive vertices which means when $2$ non-consecutive vertices are joined that becomes a diagonal.

Note: Diagonal of any polygon can be calculated when the number of sides or vertices are known to us. The sum of all the interior angles of a hexagon is $720$ degrees where each angle can be calculated by using the formula $180\left( {n - 2} \right)$ where n is the number of sides of a polygon. Here for hexagon$= 6$, each angle of hexagon is $180\left( {6 - 2} \right)$ which results into $180 \times 4$ gives ${720^o}$ .