Two goats are tied to two adjacent corners of a square plot side 28 m with ropes each 14 m long . Find the area not grazed by the goats in the plot in `m^(2)`

Options

A. 168
B. 476
C. 376
D. 238

Answer

To solve the problem of finding the area not grazed by the two goats tied to adjacent corners of a square plot, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the dimensions of the square plot:**
- The side length of the square plot is given as 28 m.

2. **Calculate the area of the square plot:**
\[ \text{Area of the square} = \text{side} \times \text{side} = 28 \, m \times 28 \, m = 784 \, m^2 \]

3. **Determine the grazing area for each goat:**
- Each goat is tied with a rope of length 14 m. Since they are tied at adjacent corners, they can graze in a quarter circle (90 degrees) from each corner.
- The radius of the grazing area for each goat is 14 m.

4. **Calculate the area grazed by one goat:**
\[ \text{Area grazed by one goat} = \frac{1}{4} \times \pi r^2 = \frac{1}{4} \times \pi \times (14 \, m)^2 \]
\[ = \frac{1}{4} \times \pi \times 196 \, m^2 = \frac{196\pi}{4} = 49\pi \, m^2 \]

5. **Calculate the total grazed area by both goats:**
- Since both goats graze the same area:
\[ \text{Total grazed area} = 49\pi + 49\pi = 98\pi \, m^2 \]

6. **Calculate the area not grazed by the goats:**
\[ \text{Area not grazed} = \text{Area of the square} - \text{Total grazed area} \]
\[ = 784 \, m^2 - 98\pi \, m^2 \]

7. **Substituting the value of \(\pi\) (approximately \(\frac{22}{7}\)):**
\[ 98\pi \approx 98 \times \frac{22}{7} = \frac{2156}{7} \approx 308.0 \, m^2 \]

8. **Final calculation for area not grazed:**
\[ \text{Area not grazed} \approx 784 \, m^2 - 308.0 \, m^2 = 476.0 \, m^2 \]

### Final Answer:
The area not grazed by the goats in the plot is approximately **476 m²**.