Number of diagonals in a 30 sided convex polygon will be-

Options

A. 405
B. 955
C. 818
D. 378

Answer

To find the number of diagonals in a 30-sided convex polygon, we can use the formula for calculating the number of diagonals in a polygon, which is given by:

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

where \( n \) is the number of sides of the polygon.

### Step-by-Step Solution:

1. **Identify the number of sides (n)**:
We are given a polygon with 30 sides, so \( n = 30 \).

2. **Substitute n into the formula**:
We will substitute \( n \) into the formula for the number of diagonals:
\[ \text{Number of diagonals} = \frac{30(30-3)}{2} \]

3. **Calculate \( n - 3 \)**:
First, calculate \( 30 - 3 \):
\[ 30 - 3 = 27 \]

4. **Multiply n by (n - 3)**:
Now, multiply \( 30 \) by \( 27 \):
\[ 30 \times 27 = 810 \]

5. **Divide by 2**:
Finally, divide \( 810 \) by \( 2 \):
\[ \frac{810}{2} = 405 \]

Thus, the number of diagonals in a 30-sided convex polygon is **405**.

### Final Answer:
The number of diagonals in a 30-sided convex polygon is **405**.

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