If (#x) represents the area of a semicircle with diameter x, then (#2)

Question

If (#x) represents the area of a semicircle with diameter x, then (#2) + (#4) =

A. (#3) 
B. (#5)
C.  (#3 \sqrt{2}) 
D.  (#2 \sqrt{5}) 
E. (#6)

pushpitkc · Answer

(#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)

pulkitarya · Answer

Hi, kindly explain why (2\sqrt{5})^2 expression been multiplied by 1/2^2 in the 2nd last line.

pushpitkc · Answer

Hi  pulkitarya

The reason I have written it like that is for better readability. It should have been

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

Hope that helps!

pulkitarya · Answer

ok, my bad..missed that totally.. thanks pushpitkc

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