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

Highlight to see answer: E

Please post your explanations in the comments below!

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Area of Rectangle = L * W

Area of Circle = Pi * r^2

30m * 40m= 1,200m so that is the area of the rectangular portion

Area of the large Circle = 400pi

Area of Shaded region = 100pi

since both areas are semicircles we must divide by 2 so..

Large semi-circle area = 200pi

Shaded semi-circle = 50pi

We must subtract -> 200pi-50pi = 150pi

so the TOTAL area is 1,200m + 150pi and the answer is E.