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Geometry Ques from GMATPrep

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by theCodeToGMAT » Wed Oct 09, 2013 3:41 am
Using Distance Formula calculate the values of sides

PQ = sqrt (4^2 + 3^2) = 5
PR = sqrt(3^2 + 4^2) = 5
QR = sqrt(7^2 + 1^2) = 5 sqrt(2)

From the above values we can see that it is a isosceles right angled triangle

So, Area = 5 * 5 /2 = 12.5
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by Brent@GMATPrepNow » Wed Oct 09, 2013 5:49 am
We're trying to find the area of triangle PQR.
Image


Let's draw a rectangle around the triangle (as shown above) and then subtract from the rectangle's area (28) the areas of the 3 right triangles that surround the triangle in question.

We get the following:
Image

So, the area of PQR = 28 - (3.5 + 6 + 6) = 12.5

Answer = A

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by pareekbharat86 » Wed Oct 09, 2013 4:30 pm
I found another formula for calculating the area of a triangle using coordinate geometry:

Area= Mod{Ax(By-Cy)+ Bx(C-Ay)+ Cx(Ay-By)}/2

Thanks everyone!
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by s.vishnu » Thu Oct 10, 2013 11:39 am
Hi,
I used a rough approach for this question.I approximated the height to be the average of the y-coordinates of(0,3) and (7,4),coming to 3.5.

I also approximated the length of this line segment as 7 instead of a more accurate sqrt50.

Area = 7X3.5)/2 =24.5/2 apprx=12.5

Probably a little lucky here..
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