#### Answer

$6.25\pi$

#### Work Step by Step

Use the distance formula to find the diameter.
$d=\sqrt{(5-2)^2+(5-1)^2}$
$d=\sqrt{(3)^2+(4)^2}$
$d=\sqrt{9+16}$
$d=\sqrt{25}$
$d=5$
The radius(r) is half the diameter, so r=2.5.
Use the formula for the area of a circle.
$A=\pi r^2=\pi (2.5)^2=\pi (6.25)=6.25\pi$