No. of diagonals of a hexagon are:

Options

A. 6
B. 9
C. 12
D. None of these

Answer

To find the number of diagonals in a hexagon, we can use a systematic approach. Here’s a step-by-step solution:

### Step 1: Understand the properties of a hexagon
A hexagon has 6 vertices (points). We denote the vertices as A, B, C, D, E, and F.

**Hint:** Remember that a diagonal connects two non-adjacent vertices.

### Step 2: Calculate the total number of line segments
From each vertex, you can connect to 5 other vertices (since there are 6 vertices in total). Therefore, if you consider all the connections from each vertex, you would have:

\[ \text{Total connections} = 6 \times 5 = 30 \]

**Hint:** This counts all line segments, including both sides of the hexagon and diagonals.

### Step 3: Adjust for double counting
Each line segment (whether a side or a diagonal) has been counted twice (once from each endpoint). Therefore, we need to divide the total by 2:

\[ \text{Total line segments} = \frac{30}{2} = 15 \]

**Hint:** This gives you the total number of line segments, including both sides and diagonals.

### Step 4: Subtract the sides of the hexagon
A hexagon has 6 sides. To find the number of diagonals, we need to subtract the number of sides from the total line segments:

\[ \text{Number of diagonals} = 15 - 6 = 9 \]

**Hint:** The sides are not diagonals, so they must be excluded from the total.

### Final Answer
The number of diagonals in a hexagon is **9**.

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