A running track is in the shape of a rectangle with a semi-circle of radius r at each end. If the total distance around the track is 200 meters, express the area enclosed by the track as a function of the radius, r. 

So you know that you have a rectangle inside of 2 semi circles

so what you have is 

rectangle A(r) = lw

semi-circle: A(r) = 1/2(πr^2) since full circle is just πr^2

and total area is 200 

so you have the area total is 200 = bh + pir^2

so u subtract 200 - pir^2 = area of a rectangle as a function of what's inside the two semi circles.