1. State the problem.\n\nA dog is leashed to a corner of a house with leash length $20$ ft, and the running area is a quarter-circle outside the corner. Find the running area.\n\n2. Write the formula.\n\nFor a full circle, area is $A=\pi r^2$.\n\nFor a quarter-circle, the area is $A=\dfrac{1}{4}\pi r^2$.\n\n3. Substitute the given radius $r=20$.\n\n$A=\dfrac{1}{4}\pi (20)^2$\n\n4. Square the radius.\n\n$20^2=400$\n\nSo $A=\dfrac{1}{4}\pi \cdot 400$\n\n5. Simplify the fraction (showing cancellation).\n\n$A=\cancel{\dfrac{1}{4}}\pi \cdot \cancel{\dfrac{400}{1}}$\n\n$A=\pi \cdot 100$\n\n6. Final answer (exact and approximate).\n\nRunning area $=100\pi$ square ft $\approx 314.16$ square ft.