The side of a rhombus is 10 cm and one diagonal is 16 cm. The area of the rhombus is

Options

A. 96 `cm^(2)`
B. 95 `cm^(2)`
C. 94 `cm^(2)`
D. 93 `cm^(2)`

Answer

To find the area of the rhombus given that the side length is 10 cm and one diagonal is 16 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Side length of the rhombus (s) = 10 cm
- One diagonal (d1) = 16 cm

2. **Determine the half-length of the diagonal**:
- Since the diagonals of a rhombus bisect each other, half of diagonal d1 will be:
\[ \frac{d1}{2} = \frac{16}{2} = 8 \text{ cm} \]

3. **Use the Pythagorean theorem**:
- In a rhombus, the diagonals form right triangles. We can find the other half of the diagonal (d2/2) using the Pythagorean theorem:
\[ s^2 = \left(\frac{d1}{2}\right)^2 + \left(\frac{d2}{2}\right)^2 \]
- Plugging in the values:
\[ 10^2 = 8^2 + \left(\frac{d2}{2}\right)^2 \]
\[ 100 = 64 + \left(\frac{d2}{2}\right)^2 \]
- Rearranging gives:
\[ \left(\frac{d2}{2}\right)^2 = 100 - 64 = 36 \]
- Taking the square root:
\[ \frac{d2}{2} = 6 \text{ cm} \]
- Therefore, the full length of diagonal d2 is:
\[ d2 = 2 \times 6 = 12 \text{ cm} \]

4. **Calculate the area of the rhombus**:
- The area (A) of a rhombus can be calculated using the formula:
\[ A = \frac{1}{2} \times d1 \times d2 \]
- Substituting the values of the diagonals:
\[ A = \frac{1}{2} \times 16 \times 12 \]
\[ A = \frac{1}{2} \times 192 = 96 \text{ cm}^2 \]

### Final Answer:
The area of the rhombus is **96 cm²**.