The number of diagonals of a polygon having 12 sides is :

Question

Accepted Answer

To determine the number of diagonals in a polygon with 12 sides, we use the formula for calculating the number of diagonals in an n-sided polygon:

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

where $ n $ is the number of sides of the polygon.

For a polygon with 12 sides:

$$ n = 12 $$

Substitute 12 into the formula:

$$ \text{Number of diagonals} = \frac{12(12-3)}{2} $$

$$ = \frac{12 \times 9}{2} $$

$$ = \frac{108}{2} $$

$$ = 54 $$

Thus, the number of diagonals in a polygon with 12 sides is 54. Therefore, Option 2 is indeed the correct answer.

Now, let's explain why the other options are incorrect:

1. **Option 1: 48** - This option is incorrect because, as calculated above, the formula yields 54 diagonals, not 48. The calculation does not support this number.

2. **Option 3: 64** - This option is incorrect because the formula clearly shows that the number of diagonals is 54, not 64. The calculation does not support this number.

3. **Option 4: 66** - This option is incorrect because the formula results in 54 diagonals, not 66. The calculation does not support this number.

In conclusion, the correct number of diagonals for a polygon with 12 sides is 54, which corresponds to Option 2.