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)
• Each vertex of an n-sided polygon can be joined to n – 3 others by a diagonal (not to itself or its two neighbours), and each diagonal is counted twice.
• Number of diagonals = n(n – 3) ÷ 2.
• For an octagon, n = 8: 8 × 5 ÷ 2 = 20, option (a).
Why the other options are wrong
- (b) 24
- 24 does not equal 8 × 5 ÷ 2.
- (c) 28
- 28 is the number of all line segments joining 8 points (8 × 7 ÷ 2), which includes the 8 sides.
- (d) 64
- 64 is 8 × 8 and has no meaning here.
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.