1. **Problem Statement:** A horse is tied to a peg at one corner of a square field with side length 15 m by a rope of length 5 m. We need to find the area of the part of the field where the horse can graze. 2. **Understanding the problem:** The horse can graze in a circular area with radius equal to the rope length, but since the rope is tied at the corner of the square field, the grazing area is limited to a quarter circle inside the field. 3. **Formula used:** The area of a circle is given by $$A = \pi r^2$$. Since the horse can only graze in a quarter circle, the grazing area is $$\frac{1}{4} \pi r^2$$. 4. **Calculation:** - Rope length (radius) $$r = 5$$ m - Area of quarter circle $$= \frac{1}{4} \pi (5)^2 = \frac{1}{4} \pi \times 25 = \frac{25\pi}{4}$$ 5. **Final answer:** The area of the field where the horse can graze is $$\frac{25\pi}{4} \approx 19.63$$ square meters. This area is fully inside the field since the rope length is less than the side of the square.