Find the ara of a kite whose diagonals measure 6 cm and 15 cm

Options

A. `60 cm^(2)`
B. ` 45 cm^(2)`
C. ` 90 cm^(2)`
D. ` 22 . 5 cm^(2)`

Answer

To find the area of a kite given the lengths of its diagonals, we can use the formula:

\[ \text{Area} = \frac{1}{2} \times D_1 \times D_2 \]

where \(D_1\) and \(D_2\) are the lengths of the diagonals.

### Step-by-Step Solution:

1. **Identify the lengths of the diagonals**:
- From the question, we have:
- \(D_1 = 6 \, \text{cm}\)
- \(D_2 = 15 \, \text{cm}\)

2. **Substitute the values into the area formula**:
- Using the formula for the area of a kite:
\[ \text{Area} = \frac{1}{2} \times D_1 \times D_2 \]
- Substitute the values:
\[ \text{Area} = \frac{1}{2} \times 6 \times 15 \]

3. **Calculate the multiplication**:
- First, calculate \(6 \times 15\):
\[ 6 \times 15 = 90 \]

4. **Divide by 2**:
- Now, divide 90 by 2:
\[ \text{Area} = \frac{90}{2} = 45 \, \text{cm}^2 \]

5. **Final Result**:
- The area of the kite is \(45 \, \text{cm}^2\).