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In the rectangular coordinate system above...

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by BTGmoderatorLU » Wed Dec 20, 2017 2:08 pm
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In the rectangular corrdinate system above, for which of the shaded regions is the area 2?

A. None
B. Q Only
C. Q and R
D. P, Q and R only
E. P, Q, R and S

The OA is D.

I should determine single each area, for example, for the triangular regions will be 1/2*B*H (where B is the base and H the height of the triangle), and for the rectangular region will be L*W (where L is the long and W the width of the rectangle), and for the square region will be L^2, right?

My question, is there another way (fast way) to solve this PS question? Experts, can you assist me with it? Thanks in advanced.
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by EconomistGMATTutor » Thu Dec 21, 2017 5:48 am
Hello LUANDATO.

You have to calculate each area. You're right about what you're thinking.

The triangle P. $$Base=4,\ Height=1\ \ \ then\ \ \ Area=\frac{4\cdot1}{2}=2.$$ The rectangle Q. $$Length\ =1,\ Width=2\ \ \ then\ \ \ Area=1\cdot2=2.$$ The scuare R. The side is the hypotenuse of a right triangle with cathetus equals to 1. So $$L=\sqrt{2},\ then\ \ \ \ Area=\left(\sqrt{2}\right)^2=2.$$ Finally, the triangle S. $$Base=3,\ Height\ =1,\ \ \ then\ \ \ Area\ =\frac{3\cdot1}{2}=\frac{3}{2}=1.5.$$ In conlcusion, the correct answer is D.

I hope this explanation may help you.

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

Regards.
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Re: In the rectangular coordinate system above...

by Scott@TargetTestPrep » Mon Mar 09, 2020 3:38 am
BTGmoderatorLU wrote: ↑
Wed Dec 20, 2017 2:08 pm
 Image

In the rectangular corrdinate system above, for which of the shaded regions is the area 2?

A. None
B. Q Only
C. Q and R
D. P, Q and R only
E. P, Q, R and S

The OA is D.
Observe that the area of each small square formed by the gridlines is 1.

The area of region P is 2 since P is a triangle with base = 4 and height = 1. Thus, the area of P is (1/2)(4)(1) = 2.

The area of region Q is 2 since Q is a rectangle with length = 2 and width = 1. Thus, the area of Q is (2)(1) = 2.

The area of region R is 2 since R can be broken into four right triangles, each of which has an area of exactly 1/2.

The area of region S, however, is not 2. We can see that S is a triangle with base = 3 and height = 1. Thus, the area of S is (1/2)(3)(1) = 3/2.

Answer: D

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