Trignometry problem

[camitava]

Again a trignometric problem ...

18. The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?
(A) 1,350π
(B) 1,200 + 400π
(C) 1,200 + 300π
(D) 1,200 + 200π
(E) 1,200 + 150π

To me, C is coming as the correct choice. But in the answer, it is saying that the OC is E. How and why, friends?

[mschling52]

I agree with C.

Area of rectangle = 1200
Area of semicircle = 400(pi)
Area of shaded = 100(pi)

Total w/o shaded = 1200+400(pi)-100(pi) = 1200+300(pi)

[tanyajoseph]

Area of rect = 1200
Area of Outer CIRCLE - 400pi
Area of Inner CIRCLE - 100pi

So area of semicircle excluding inner circle should be either (400pi-100pi)/2
or 400pi/2 - 100pi/2 which would both give 150 pi.
So answer would be 1200 + 150 pi --->E

Key: The catch is to calculate the area of semicircle and not the area of circle

[kajcha]

Should be E

[camitava]

Ohhhhh! Now got it. Thanks a lot friends. Look another example of overlook and carelessness. While solving the problem, I really forgot that we are dealing with semi-circles not a circle! Look how careless I am.

[niks_01.27]

I always write on the scratch paper things like "semi-circle" here, that helps. You can also try it out.