Explanation:

- The goat is tied to one corner of an equilateral triangle-shaped plot.

- The rope's length is 10.5 meters.

- The goat can graze in a circular area with a radius equal to the rope's length.

- The area of this circle is calculated using the formula \( \pi \times \text{radius}^2 \).

- Since the plot is equilateral and the goat can only graze reaching over part of it as its roaming area overlaps outside the triangle, it forms a sector of the circle.

- In \(120^\circ\,\) (1/3 of the circle), the grazable area is \(\frac{1}{3} \times \pi \times (10.5)^2 \approx 115.5 \, \text{m}^2 \).

- The overlap areas outside need subtraction. It accounts for roughly half inside the triangle.

- Option 2: 57.75 m²