112) What is the area of the shaded region

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112) What is the area of the shaded region

by ern5231 » Sun May 16, 2010 8:50 pm
In the figure shown, each side of the square has the length 1m. What is the area of the shaded regoin.

I am sorry i don't have the options.
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by sk818020 » Sun May 16, 2010 9:01 pm
There would need to be more info to derive this answer. I believe there would also need to calculus involved if you had the right information to figure out the question. GMAT doesn't do either of these.

The question doesn't give you any values at all so it would be impossible to determine what the exact area of the shaded region is.

Hope that helps.

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by kstv » Sun May 16, 2010 11:33 pm
Lets the answer options be


1) TT +1
2) TT -1
3) 1
4) TT/2 -1
5) TT/2 - 1/2


TT is the symbol, pie = 22/7 app.

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by kuntalkkc » Mon May 17, 2010 11:48 am
quite easy...

half of the shaded region=area of quarter circle-half area of sq=Pi*1/4-1/2
total shaded region=2(pi/4-1/2)=pi/2-1=TT/2-1...ans option 4....any doubt?

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by indiantiger » Mon May 17, 2010 12:52 pm
each BCA and DCA represents 1/4 of a circle with radius = 1

lets calculate the area of the sector = angle/360 22/7 (1)^2

shaded area = area of square - (area of square - area of the sector BCA) - (area of the circle - area of the sector DCA)
= 1 - (1-90/360*TT*1) -(1-90/360*TT*1)
= 1-1-1+TT/4+TT/4
= TT/2 - 1


*TT = 22/7

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by [email protected] » Mon May 17, 2010 2:55 pm
kuntalkkc wrote:quite easy...

half of the shaded region=area of quarter circle-half area of sq=Pi*1/4-1/2
total shaded region=2(pi/4-1/2)=pi/2-1=TT/2-1...ans option 4....any doubt?
How do you know the two arcs are quarter-circles?

I agree that if we had that information we could solve, but the question doesn't include that info and we certainly can't (and are never expected to) make any assumptions of that nature on the GMAT.
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