How many diagonals are there in a polygon having 12 sides ?

Options

A. 12
B. 24
C. 36
D. 54

Answer

To find the number of diagonals in a polygon with 12 sides, we can use the formula for calculating the number of diagonals in a polygon:

**Step 1: Identify the number of sides (n) of the polygon.**
Here, the polygon has 12 sides, so we have:
\( n = 12 \)

**Step 2: Use the formula for the number of diagonals.**
The formula to calculate the number of diagonals (D) in a polygon is:
\[ D = \frac{n(n - 3)}{2} \]

**Step 3: Substitute the value of n into the formula.**
Now, we will substitute \( n = 12 \) into the formula:
\[ D = \frac{12(12 - 3)}{2} \]

**Step 4: Simplify the expression inside the parentheses.**
Calculate \( 12 - 3 \):
\[ 12 - 3 = 9 \]
Now substitute this back into the formula:
\[ D = \frac{12 \times 9}{2} \]

**Step 5: Calculate the product of 12 and 9.**
Now calculate \( 12 \times 9 \):
\[ 12 \times 9 = 108 \]
So we have:
\[ D = \frac{108}{2} \]

**Step 6: Divide by 2 to find the number of diagonals.**
Now divide 108 by 2:
\[ D = 54 \]

Thus, the number of diagonals in a polygon with 12 sides is **54**.

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