Explanation
Without the house the running area would form a circle with a 14 ft radius. Since the corners of the house describe a 90° angle then the house covers a quarter of the entire circle. Therefore the running area will be three quarters of the area of a 14 ft radius circle. The area if a circle with radius r is given by:
[tex]A=\pi r^2[/tex]
Then 3 quarters of the area of a 14 ft radius circle are given by:
[tex]\frac{3}{4}\cdot A=\frac{3}{4}\cdot\pi\cdot(14ft)^2=461.81ft^2[/tex]Answer
We must round the answer to the nearest square foot. Then the answer is:
The dog has about 462 square feet of running area.
