A rectangular field measures 25 m by 14 m. Along the side measuring 14 m, a semicircular platform with the diameter along the side of the field is made. Find the area of the remaining field.

Answer

To find the area of the remaining field after a semicircular platform is made, we can follow these steps:

### Step 1: Calculate the area of the rectangular field.
The formula for the area of a rectangle is:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given the dimensions of the rectangular field are 25 m (length) and 14 m (breadth):
\[ \text{Area of rectangle} = 25 \, \text{m} \times 14 \, \text{m} = 350 \, \text{m}^2 \]

### Step 2: Determine the radius of the semicircle.
The semicircular platform is made along the side measuring 14 m. The diameter of the semicircle is equal to the length of this side, which is 14 m. Therefore, the radius \( r \) of the semicircle is:
\[ r = \frac{\text{Diameter}}{2} = \frac{14 \, \text{m}}{2} = 7 \, \text{m} \]

### Step 3: Calculate the area of the semicircle.
The formula for the area of a semicircle is:
\[ \text{Area of semicircle} = \frac{1}{2} \pi r^2 \]
Substituting the value of \( r \):
\[ \text{Area of semicircle} = \frac{1}{2} \times \pi \times (7 \, \text{m})^2 = \frac{1}{2} \times \pi \times 49 \, \text{m}^2 \]
Using \( \pi \approx \frac{22}{7} \):
\[ \text{Area of semicircle} = \frac{1}{2} \times \frac{22}{7} \times 49 \, \text{m}^2 = \frac{22 \times 49}{14} \, \text{m}^2 = 77 \, \text{m}^2 \]

### Step 4: Calculate the area of the remaining field.
To find the area of the remaining field, subtract the area of the semicircle from the area of the rectangle:
\[ \text{Area of remaining field} = \text{Area of rectangle} - \text{Area of semicircle} \]
Substituting the values:
\[ \text{Area of remaining field} = 350 \, \text{m}^2 - 77 \, \text{m}^2 = 273 \, \text{m}^2 \]

### Final Answer:
The area of the remaining field is \( 273 \, \text{m}^2 \).

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