If the dog were on a 15-ft leash tied to a stake in the ground
out in the middle of a field, then he could cover every blade
of grass in a 15-ft circle. The area of a circle is (pi R²), so
he would have free range over (pi · 15²) square feet of area.
Sadly, he's not out in the middle of a field. He's tied to the corner
of the house. So he can't cover the whole circle, because the house
blocks a quarter of the circle. The dog only has access to
(3/4) of (pi R²)
= (0.75) · π · (15²)
= (0.75 · π · 225) = 530 square feet (rounded)