Question

The number of diagonal in a polygon of $n$ sides is:

• A. $\frac{n(n-3)}{2}$
• B. ${}^{n}C_{2}$
• C. $n(n-3)$
• D. $\frac{n(n-1)}{2}$

Hint:

A triangle ($n=3$) has 0 diagonals, which matches the formula: $3(0)/2 = 0$.

Answer 1

The Correct Option is A

Step 1: Concept
Total lines between $n$ points is ${}^{n}C_2$. Diagonals are these lines minus the sides.
Step 2: Analysis
Diagonals $= {}^{n}C_{2} - n = \frac{n(n-1)}{2} - n$.
$= \frac{n^2 - n - 2n}{2}$.
Step 3: Conclusion
$= \frac{n^2 - 3n}{2} = \frac{n(n-3)}{2}$.
Final Answer: (A)