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Geometry - help!

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Junior | Next Rank: 30 Posts
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by ahahkhyati.j » Mon Oct 19, 2015 2:19 pm
Hi
can someone help me solve the following question. Thanks.


Image

If each curved portion of the boundary of the figure above is formed from circumferences of two semicircles, each with radius 2 and each of the parallel sides have length 4. What is the are of shaded region?

(A) 18
(B) 32
(C) 16 - 8Pi
(D) 32 - 8Pi
(E) 32 - 4pi

Ans: B

I took the breadth and length as 4 and 2Pi*r because it is formed from the circumference of two semicircles. Where am i going wrong?
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by theCEO » Mon Oct 19, 2015 5:18 pm
ahahkhyati.j wrote:Hi
can someone help me solve the following question. Thanks.


Image

If each curved portion of the boundary of the figure above is formed from circumferences of two semicircles, each with radius 2 and each of the parallel sides have length 4. What is the are of shaded region?

(A) 18
(B) 32
(C) 16 - 8Pi
(D) 32 - 8Pi
(E) 32 - 4pi

Ans: B

I took the breadth and length as 4 and 2Pi*r because it is formed from the circumference of two semicircles. Where am i going wrong?
Image

Notice from the rectangle, that the area of the semicircles outside the rectangle = area of missing space inside the rectangle
Width = 4
Length = 2 x 2r = 8
Area = 8 x 4 = 32

ans = b
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by MartyMurray » Wed Oct 21, 2015 8:54 pm
ahahkhyati.j wrote:I took the breadth and length as 4 and 2Pi*r because it is formed from the circumference of two semicircles. Where am i going wrong?
You used the perimeter of the top and bottom sections as the length of them, whereas actually the perimeter is not the same as the length in this case.
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by [email protected] » Thu Oct 22, 2015 9:57 am
Hi ahahkyati.j,

As theCEO has shown, it helps to think about the given shape in a different way. Whenever Geometry questions involve a 'strange' shape, it often helps to think about how you could change the shape by breaking it down into 'pieces.' While you won't have to use that particular Tactic too often on Test Day, it can be quite useful when dealing with certain tougher Geometry prompts.

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