The graph of f(x)= (0.5)^x is replaced by the graph of g(x) = (0.5)^x-k. if g(x) is obtained by shifting f(x) down 2 units, then what is the value of k?

a) k=2
b) k=1/2
c) k= -2
d) k= -1/2

Well, what I would do [not sure if it's the correct way], is use the white area as a sector of a circle. The top right of the box is the center of the circle, so the radius is 6.
Then, by the white portion being one quarter of the circle (90° out of 360°), I could calculate the that pink shaded region = the total square (6×6) minus the white sector.
So area (A) of white sector (s): A(s) = 1/4×pi×r^2

36 - 28.27 = 7.73