(#x) represents the area of a semicircle with diameter x.

Formula:

Area of a semicircle = \(\frac{1}{2}\)*pi*r^2 where r-radius or diameter/2

(#2) = \(\frac{1}{2}*pi*1^2\)

(#4) = \(\frac{1}{2}*pi*2^2\)

(#2) + (#4) = \(\frac{1}{2}*pi*(1+4)\) = \(\frac{1}{2}*pi*{5}\)

\((#2 \sqrt{5})\) = \(\frac{1}{2}*pi*{2\sqrt{5}}^2*\frac{1}{2^2}\) = \(\frac{1}{8}*pi*{4*5}\) = \(\frac{1}{2}*pi*{5}\)

Therefore, (#2) + (#4) = \((#2 \sqrt{5})\)(Option D)

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