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Rectangle ABCD has a perimeter of 26. The half circle...

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by BTGmoderatorLU » Sat Nov 25, 2017 8:43 am
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Rectangle ABCD has a perimeter of 26. The half circle with diameter AD has an area of 8Ï€. What is the perimeter of the part of the figure that is not shaded?

A. 26 + 4Ï€
B. 18 + 8Ï€
C. 18 + 4Ï€
D. 14 + 4Ï€
E. 14 + 2Ï€

The OA is C.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
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by EconomistGMATTutor » Sat Nov 25, 2017 9:29 am
Hello LUANDATO.

Let's see your question.

The area of the half circle is 8Ï€, so the complete circle would have an area of 16Ï€. It implies that r=AD/2=4.

So, AD=8.

By the other hand, AB+BC+CD+DA=2AB+2AD=2AB+2*8=2AB + 16 = 26. It implies that 2AB=10, so AB=5.

Now, the lenght of the arc AD is equal to π*r, that is to say, 4π.

Finally, the perimeter is $$AB+BC+CD+arc\left(AD\right)=5+8+5+4\pi=18+4\pi.$$ So, the correct answer is C .

I really hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.
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