In an Octagon the number of possible diagonals are ?
2023
In an Octagon the number of possible diagonals are ?
- A.
20
- B.
24
- C.
28
- D.
18
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Use the standard formula for diagonals in an n-sided polygon: n(n − 3)/2.
For an octagon, n = 8, so the number of diagonals is 8 × (8 − 3) / 2 = 8 × 5 / 2 = 20.
Alternate check: number of line segments joining any two vertices is C(8,2) = 28. Subtract the 8 sides to obtain 28 − 8 = 20 diagonals.