The diagonal of the square field measures 50m. The area of square field is?

Options

A. a. 1250m^2
B. b. 1200m^2
C. c. 1205m^2
D. d. 1025m^2

Answer

To find the area of the square field given that its diagonal measures 50 meters, we can use the formula for the area of a square in terms of its diagonal.

### Step-by-Step Solution:

1. **Understand the relationship between the diagonal and the area of a square**:
The area \( A \) of a square can be calculated using the formula:
\[ A = \frac{1}{2} \times d^2 \]
where \( d \) is the length of the diagonal.

2. **Substitute the value of the diagonal**:
Given that the diagonal \( d \) is 50 meters, we substitute this value into the formula:
\[ A = \frac{1}{2} \times (50 \, \text{m})^2 \]

3. **Calculate \( (50 \, \text{m})^2 \)**:
\[ (50 \, \text{m})^2 = 2500 \, \text{m}^2 \]

4. **Calculate the area**:
Now substitute \( 2500 \, \text{m}^2 \) back into the area formula:
\[ A = \frac{1}{2} \times 2500 \, \text{m}^2 = 1250 \, \text{m}^2 \]

5. **Final Answer**:
Therefore, the area of the square field is:
\[ A = 1250 \, \text{m}^2 \]