Question

Find the number of diagonals of a hexagon.

Answer 1

Hint: 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 \[{720^o}\] .