Question

Find the number of diagonals of a polygon of 10 sides?

Answer 1

Hint: We have given a polygon of 10 sides and we have to find the number of diagonals of the polygon. Firstly we take a polygon of ‘n’ side and find the number of diagonals that can be drawn in that polygon. We will get a formula for finding the number of diagonals of the polygon with variable ‘\[n\]’. We put the value of \[n{\text{ }} = {\text{ }}10\]. We will get the number of diagonals of a polygon of side 10.

Complete step by step answer:
We have given a polygon.
Sides of polygon = 10
We have to find the number of diagonals of the polygon of 10 sides
Firstly we will find the number of diagonals of the polygon of \[n\] sides.
Let us consider a polygon of ‘\[n\]’ sides
Number of vertices of polygon = \[n\]
Now if we take a fixed vertex from which we have to draw the diagonal then we cannot draw the diagonal from this point to their adjacent point.
So there are three vertices on which diagonals cannot be drawn. Now one diagonal is counted two times. So 10 number of possible diagonals for the polygon of n sides= \[\dfrac{{nx(n - 3)}}{2}\]
Now we have a number of sides = 10
So the number of diagonals = \[\dfrac{{10 \times (10 - 3)}}{2}\]=35

Note: Polygon: In geometry, a polygon is a plane figure which is described by a finite number of straight-line segments connected to form a closed polygonal chain or polygonal circuit.
Diagonal: A straight line joining two vertices of the polygon is called a diagonal.