Question

How many diagonals are there in a decagon?

Answer 1

Hint:In this question use the direct formula to find the number of diagonals $d = \dfrac{{n\left( {n - 3} \right)}}{2}$where n is the number of number of sides of decagon. The sides of the decagon are 10.

Complete step-by-step answer:

In geometry a Decagon is a ten-sided polygon or 10-gon as shown in figure.
A regular decagon has all sides of equal length and each internal angle will always be equal to ${144^0}$ as shown in figure.
The general formula for number of diagonals (d) in any figure are
(n-3) multiply by the number of vertices and divide by 2.
$\Rightarrow d = \dfrac{{n\left( {n - 3} \right)}}{2}$ ( where n is the number of vertices)
As we know in a decagon there are ten sides (see figure)
$\Rightarrow n = 10$
Therefore number of diagonals in a decagon are
$\Rightarrow d = \dfrac{{n\left( {n - 3} \right)}}{2} = \dfrac{{10\left( {10 - 3} \right)}}{2} = \dfrac{{10 \times 7}}{2} = 35$
So the number of diagonals in a decagon are 35.
So this is the required answer.

Note – A decagon is a closed shape with ten edges and ten vertices. All sides of a regular decagon are of the same length. All the corners added together equal ${1440^0}$. It is a closed quadrilateral. It is generally advised to remember the direct formula as it helps solving problems of this kind in a short span of time.