Length of diagonals of a rhombus field are 8 m and 14 m. Find its area

Options

A. 56 sq m
B. 58 sq m
C. 60 sq m
D. 62 sq m

Answer

To find the area of a rhombus when the lengths of its diagonals are given, 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**:
- Given \(d_1 = 8 \, \text{m}\) (first diagonal)
- Given \(d_2 = 14 \, \text{m}\) (second diagonal)

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 = \frac{1}{2} \times 8 \times 14 \]

3. **Calculate the product of the diagonals**:
\[ 8 \times 14 = 112 \]

4. **Divide by 2 to find the area**:
\[ \text{Area} = \frac{112}{2} = 56 \, \text{m}^2 \]

5. **Final result**:
The area of the rhombus is \(56 \, \text{m}^2\).