The spread of oil leaking in the ocean is the form of a circle. If the radius of the oil spread after t\displaystyle {t} hours is r(t)=170t\displaystyle {r}{\left({t}\right)}={170}\sqrt{{{t}}}, find the area of the oil spread in terms of time t\displaystyle {t}.

A(t)=\displaystyle {A}{\left({t}\right)}=