Question

The number of diagonals that can be drawn in a polygon of 100 sides is
a. 4850
b. 4950
c. 9900
d. 98

Answer 1

Hint: In order to solve this question, we should remember that for an n sided polygon, each vertex can draw (n - 3) diagonals because any vertex cannot draw a diagonal to itself and also it cannot draw a diagonal to its predecessor and successor vertices. Also, we need to remember that each diagonal would be drawn twice if we draw all the possible diagonals from each possible point. By using this concept, we can find the answer to this question.

Complete step-by-step answer:
In this question, we have been asked to find the number of diagonals that can be drawn for a polygon of 100 sides. To solve this question, we should know that each vertex of every n sided polygon draws (n - 3) diagonals because it cannot draw a diagonal to itself and the predecessor and successor vertices. So, we can say that the total number of diagonals that can be drawn are n (n - 3). Now, we know that each diagonal will be drawn twice (to and from each vertex). So, the total number of diagonals in any n sided polygon will be $\dfrac{n\left( n-3 \right)}{2}$.
So, we can say that, for a 100 sided polygon, that is for n = 100, we get,
Number of diagonals for 100 sided polygon = $\dfrac{100\left( 100-3 \right)}{2}=50\times 97=4850$.
Hence, we can say that a 100 sided polygon will have 4850 diagonals. Therefore, option (a) is the correct answer.

Note: We can directly solve this question by applying the formula of the number of diagonals for n sided polygon, that is, $\dfrac{n\left( n-3 \right)}{2}$. Also, we cannot even think of drawing a figure and solving it for a 100 sided polygon. So, it is better to remember the formula.