What is the number of diagonals of an octagon?

• (a) 48
• (b) 40
• (c) 28
• (d) 20

To find the number of diagonals in an octagon, we can use a specific formula. For any polygon with \( n \) sides, the number of diagonals can be calculated using the formula:

Diagonal Formula

Number of diagonals = \( \frac{n(n - 3)}{2} \)

Applying the Formula

In the case of an octagon, \( n = 8 \). Plugging this value into the formula gives:

• Number of diagonals = \( \frac{8(8 - 3)}{2} \)
• Number of diagonals = \( \frac{8 \times 5}{2} \)
• Number of diagonals = \( \frac{40}{2} \)
• Number of diagonals = 20

Final Answer

Therefore, the number of diagonals in an octagon is 20. The correct option is (d) 20.