Mabel is installing a square pool in her backyard and wants a circular fence to enclose the pool to create 4 grassy areas around the pool as show in the figure. If the pool is located at the coordinates (1, 5), (5, 8), (4, 1), and (8, 4), what is the amount of fencing Mabel needs to purchase? Round your answer to the nearest tenth. (Like 5.7 or 3.4).

Question

Mabel is installing a square pool in her backyard and wants a circular fence to enclose the pool to create 4 grassy areas around the pool as show in the figure.  If the pool is located at the coordinates (1, 5), (5, 8), (4, 1), and (8, 4), what is the amount of fencing Mabel needs to purchase?  Round your answer to the nearest tenth.  (Like 5.7 or 3.4).

Reiny · Answer

I can't see your diagram, but the diagonal of the square from (4,1) to (5,8) is also the diameter of the circle
length = √(1^2 + 7^2) = √50 = 5√2
so the radius of the circle must be 2.5√2

perimeter of circle = 2πr or dπ
= √50π
= appr 22.2