A horse is tied to a peg at one corner of a square shaped grass field of side `15` m by means of a `5` m long rope. Find(i) the area of that part of the field in which the horse can graze.(ii) the increase in the grazing area if the rope were `10` m long instead of `5` m.

Explanation

To solve the problem step by step, we will calculate the area in which the horse can graze for both the 5 m rope and the 10 m rope.

### Step 1: Calculate the grazing area with a 5 m rope
1. **Identify the shape of the grazing area**: When the horse is tied to a peg at one corner of the square field with a 5 m rope, it can graze in a quarter-circle area (since the rope is tied at a corner).
2. **Calculate the area of the quarter-circle**:
- The formula for the area of a circle is \( A = \pi r^2 \).
- For a quarter-circle, the area will be \( A = \frac{1}{4} \pi r^2 \).
- Here, \( r = 5 \) m.
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