Diagonals of an octagon — Aptitude Question
Diagonals of an octagon: How many diagonals does a regular octagon have? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
How many diagonals does a regular octagon have?
Options
- 16
- 20
- 24
- 28
Show the answer and the worked solution
Correct answer: B. 20
Worked solution
- Lines joining any two of the 8 vertices = C(8,2) = 28.
- Of these, 8 are the sides of the octagon.
- Diagonals = 28 − 8 = 20.
Answer: 20.
The idea
Diagonals of an n-gon = n(n − 3)/2 = 8 × 5/2 = 20. Both routes agree; subtracting the sides makes the reason clear.
Shortcut. Diagonal counts for 4 to 8 sides run 2, 5, 9, 14, 20 — each extra side adds one more than the step before (+3, +4, +5, +6).
Common trap. "28" — counting every line joining two vertices, C(8,2) = 28, and forgetting that 8 of those lines are sides, not diagonals.
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