How many diagonals can be drawn by joining the vertices of an octagon?
- (a) 20 ✓ UPSC's answer
- (b) 24
- (c) 28
- (d) 64
Why the answer is (a)
• The formula for the number of diagonals in a polygon with $n$ sides is $\frac{n(n-3)}{2}$.
• For an octagon, the number of sides $n$ is 8.
• Substituting $n=8$ into the formula gives $\frac{8(8-3)}{2}$.
• This simplifies to $\frac{8 \times 5}{2} = \frac{40}{2} = 20$.
• Therefore, the total number of diagonals is 20, which corresponds to option (a).
Why the other options are wrong
- (b) 24
- Option (b) is incorrect because 24 is not the result of the diagonal formula for an octagon.
- (c) 28
- Option (c) is incorrect because 28 is the number of sides in a 10-sided polygon's diagonal count, not an octagon.
- (d) 64
- Option (d) is incorrect because 64 is the square of 8, not the number of diagonals.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.