Question

The number of diagonals that can be drawn in an octagon is:

• A. 20
• B. 28
• C. 30
• D. 15

Hint:

For any polygon with \(n\) sides, the number of diagonals can be found using the formula \(\frac{n(n-3)}{2}\).

Answer 1

The Correct Option is A

The number of diagonals that can be drawn in an octagon is:

Step 1: Formula for the number of diagonals
The formula to calculate the number of diagonals \( D \) in a polygon with \( n \) sides is: \[ D = \frac{n(n-3)}{2} \] where \( n \) is the number of sides (or vertices) of the polygon.

Step 2: Apply the formula for an octagon
An octagon has \( n = 8 \) sides. Substituting this value into the formula: \[ D = \frac{8(8-3)}{2} = \frac{8 \times 5}{2} = \frac{40}{2} = 20 \]

Step 3: Conclusion
Therefore, the number of diagonals that can be drawn in an octagon is \( \boxed{20} \).