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Manager  Joined: 06 Feb 2010
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In the rectangular coordinate system above, for which of the  [#permalink]

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Attachment: Untitled.png [ 19.84 KiB | Viewed 17869 times ]
In the rectangular coordinate 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

Attachment: Clips.jpg [ 34.76 KiB | Viewed 22097 times ]

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Originally posted by monirjewel on 22 Nov 2010, 06:29.
Last edited by Bunuel on 21 Jul 2014, 11:25, edited 1 time in total.
Edited the question
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 57281
In the rectangular coordinate system above, for which of the  [#permalink]

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1
4 In the rectangular coordinate 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 area of a rectangle equals to $$area=width*length$$;

The area of a triangle equals to $$area=\frac{1}{2}*base*height$$ (also the area of a square=diagonal^2/2);

Now it's easy to calculate the areas of given figure:
$$area_P=\frac{1}{2}*4*1=2$$;
$$area_Q=1*2=2$$;
$$area_R=\frac{2^2}{2}=2$$;
$$area_S=\frac{1}{2}*3*1=1.5$$.

Answer: D.
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Manager  Joined: 13 Jul 2011
Posts: 83
Concentration: Operations, Strategy
GMAT 1: 680 Q46 V37 WE: Engineering (Telecommunications)
Re: In the rectangular coordinate system above, for which of the  [#permalink]

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1
1
1
Area of a triangle = 1/2 * Base * Height,
from the graph we can find out length of base and height of the triangles and rectangles.
P: Base = 4 Height = 1 Area = 1/2 (4)(1) = 2
Q: Base = 1 Height = 2 Area = Base * Height = 1 * 2 = 2
R: For a rhombus area can be calculated using the value of the diagonals ( D1 * D2 ) / 2
i:e (2*2)/2 = 2
S: Base = 3 Height = 1 Area = 1/2 (3)(1) = 1.5

So answer is D Math Expert V
Joined: 02 Sep 2009
Posts: 57281
Re: In the rectangular coordinate system above, for which of the  [#permalink]

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Bumping for review and further discussion.

GEOMETRY: Shaded Region Problems!
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Posts: 234
Location: India
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GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34 Re: In the rectangular coordinate system above, for which of the  [#permalink]

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Bunuel wrote:
In the rectangular coordinate 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
E. P, Q, R and S

The area of a rectangle equals to $$area=width*length$$;

The area of a triangle equals to $$area=\frac{1}{2}*base*height$$ (also the area of a square=diagonal^2/2);

Now it's easy to calculate the areas of given figure:
$$area_P=\frac{1}{2}*4*1=2$$;
$$area_Q=1*2=2$$;
$$area_R=\frac{2^2}{2}=2$$;
$$area_S=\frac{1}{2}*3*1=1.5$$.

Answer: D.

Hey Bunuel, How did you find the area of R? Did you divide it into two triangles?
And just for curiosity is that figure a square?

I got the right answer as I figured out the area of other three and the only option suitable was D
Math Expert V
Joined: 02 Sep 2009
Posts: 57281
Re: In the rectangular coordinate system above, for which of the  [#permalink]

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2
2
b2bt wrote:
Bunuel wrote:
In the rectangular coordinate 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
E. P, Q, R and S

The area of a rectangle equals to $$area=width*length$$;

The area of a triangle equals to $$area=\frac{1}{2}*base*height$$ (also the area of a square=diagonal^2/2);

Now it's easy to calculate the areas of given figure:
$$area_P=\frac{1}{2}*4*1=2$$;
$$area_Q=1*2=2$$;
$$area_R=\frac{2^2}{2}=2$$;
$$area_S=\frac{1}{2}*3*1=1.5$$.

Answer: D.

Hey Bunuel, How did you find the area of R? Did you divide it into two triangles?
And just for curiosity is that figure a square?

I got the right answer as I figured out the area of other three and the only option suitable was D

Yes, it's a square because its diagonals are equal and perpendicular bisectors of each other. The area of a square=diagonal^2/2.

Does this make sense?

P.S. $$area_{square}=\frac{d^2}{2}$$ and $$area_{rhombus}=\frac{d_1*d_2}{2}$$.
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Intern  Joined: 20 May 2014
Posts: 32
Re: In the rectangular coordinate system above, for which of the  [#permalink]

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Bunuel wrote:
b2bt wrote:
Bunuel wrote:
In the rectangular coordinate 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
E. P, Q, R and S

The area of a rectangle equals to $$area=width*length$$;

The area of a triangle equals to $$area=\frac{1}{2}*base*height$$ (also the area of a square=diagonal^2/2);

Now it's easy to calculate the areas of given figure:
$$area_P=\frac{1}{2}*4*1=2$$;
$$area_Q=1*2=2$$;
$$area_R=\frac{2^2}{2}=2$$;
$$area_S=\frac{1}{2}*3*1=1.5$$.

Answer: D.

Hey Bunuel, How did you find the area of R? Did you divide it into two triangles?
And just for curiosity is that figure a square?

I got the right answer as I figured out the area of other three and the only option suitable was D

Yes, it's a square because its diagonals are equal and perpendicular bisectors of each other. The area of a square=diagonal^2/2.

Does this make sense?

P.S. $$area_{square}=\frac{d^2}{2}$$ and $$area_{rhombus}=\frac{d_1*d_2}{2}$$.

Bunuel for calculating area of R : how did you get 2^2 /2 , where is 2 coming from? Can you explain the counting of boxes?

same question for S and Q
Math Expert V
Joined: 02 Sep 2009
Posts: 57281
Re: In the rectangular coordinate system above, for which of the  [#permalink]

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sagnik2422 wrote:
Bunuel wrote:
Bunuel wrote:
In the rectangular coordinate 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
E. P, Q, R and S

The area of a rectangle equals to $$area=width*length$$;

The area of a triangle equals to $$area=\frac{1}{2}*base*height$$ (also the area of a square=diagonal^2/2);

Now it's easy to calculate the areas of given figure:
$$area_P=\frac{1}{2}*4*1=2$$;
$$area_Q=1*2=2$$;
$$area_R=\frac{2^2}{2}=2$$;
$$area_S=\frac{1}{2}*3*1=1.5$$.

Answer: D.

Yes, it's a square because its diagonals are equal and perpendicular bisectors of each other. The area of a square=diagonal^2/2.

Does this make sense?

P.S. $$area_{square}=\frac{d^2}{2}$$ and $$area_{rhombus}=\frac{d_1*d_2}{2}$$.

Bunuel for calculating area of R : how did you get 2^2 /2 , where is 2 coming from? Can you explain the counting of boxes?

same question for S and Q R is a square --> the area of a square=diagonal^2/2 --> diagonal of R = 2 --> area = 2^2/2.

Q is a rectangle --> the area = length*width = 1*2.

S is a triangle --> the area = 1/2*base*height = 1/2*3*1 (consider vertical side as base).

Hope it's clear.
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Intern  Joined: 20 May 2014
Posts: 32
Re: In the rectangular coordinate system above, for which of the  [#permalink]

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Great explanation, but how can I see that diagonal of R is 2? (like can you possibly label this on the diagram or give coordinates) also, I don't see how the width is 2 for the rectangle.

Sorry for the bother.
Intern  Joined: 20 May 2014
Posts: 32
Re: In the rectangular coordinate system above, for which of the  [#permalink]

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also how is the height 1 for S?
Math Expert V
Joined: 02 Sep 2009
Posts: 57281
Re: In the rectangular coordinate system above, for which of the  [#permalink]

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sagnik2422 wrote:
Great explanation, but how can I see that diagonal of R is 2? (like can you possibly label this on the diagram or give coordinates) also, I don't see how the width is 2 for the rectangle.

Sorry for the bother.

Ask yourself how many units are there in the diagonal of R, in the width of the rectangle, ...

Sorry, I don't know how to explain it better.
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Director  V
Joined: 06 Jan 2015
Posts: 696
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: In the rectangular coordinate system above, for which of the  [#permalink]

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monirjewel wrote:
Attachment:
Untitled.png
In the rectangular coordinate 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

Attachment:
Clips.jpg

Hi,

By using logic, Calculate the area of P=(1/2)bh=>(1/2)(4)(1)=>2

Now see the options and quickly eliminate A,B,C (doesn't contain P)

Now calculate Are of S=(1/2)(3)(1) is not equal to 2 hence eliminate E

Ans:D
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Manager  B
Joined: 16 May 2018
Posts: 85
Location: Hungary
Schools: Queen's MBA'20
Re: In the rectangular coordinate system above, for which of the  [#permalink]

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R is a square --> the area of a square=diagonal^2/2 --> diagonal of R = 2 --> area = 2^2/2.

About this, how did u figure that 2 is a diagonal and not a side length of square?
Director  P
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Re: In the rectangular coordinate system above, for which of the  [#permalink]

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1
People can be confused over R.

Use a right triangle to articulate side length of square R as per my diagram.
Attachments Capture.JPG [ 47.76 KiB | Viewed 599 times ]

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+1 Kudos if you like my post pls! Re: In the rectangular coordinate system above, for which of the   [#permalink] 19 Jul 2019, 19:00
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