Number of Diagonals in a Pentagon

Polygon is any shape, which is enclosed by its sides. The line segments that connect any two vertices are called as diagonals. The names of the polygon are classified on the basis of their number of sides. Any polygons which possess five sides are called as pentagon. In this article, we shall discuss about the number of diagonals of pentagon. Also we shall solve problems regarding number of diagonals of pentagon.

Formula - Number of Diagonals of Pentagon:

The number of diagonals of any polygon can be obtained by using the formula,

 [n(n-3)]/2

where n is the number of sides of the polygon.

diagonals of pentagon

Now we shall determine the number of diagonals of pentagon.

The number of sides of a pentagon is five.

Therefore n = 5.

By substituting n = 5 in the above formula, we can determine the number of diagonals of pentagon.

Number of diagonals of pentagon = [5(5-3)]/2

= [5(2)]/2

= 10/2

= 5

Therefore the number of diagonals of pentagon is 5.


Example Problem - Number of Diagonals in a Pentagon:

Determine the number of sides and name of the polygon whose number of diagonals is 5.

Solution:

Given:

The number of Diagonals = 5

The formula to determine the number of diagonals is

[n(n-3)]/2 ,

where n is the number of sides of the polygon.

We have to find n:

Equate the both.

[n(n-3)]/2 = 5

Multiply by 2 on both sides:

2[(n(n-3))/2] = 2(5)

n(n - 3) = 10

Multiply by n within the bracket:

n2 - 3n = 10

Subtract 10 on both sides.

n2 - 3n - 10 = 0

n2 - 5n + 2n - 10 = 0

n(n - 5) + 2 (n - 5) = 0

(n - 5) (n + 2) = 0

n - 5 = 0 and n + 2 = 0

n = 5 and n = -2

The sides of polygon must not be negative. So ignore -2.

Therefore the number of sides of the polygon is 5.

Pentagon is the polygon which possess 5 sides.

Hence pentagon is the polygon which possess 5 sides and 5 diagonals in it.