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In the rectangular coordinate system above, for which of the

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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

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[Reveal] Spoiler: OA

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Last edited by Bunuel on 21 Jul 2014, 10:25, edited 1 time in total.
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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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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 :)
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New post 06 Mar 2014, 01:34
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Re: In the rectangular coordinate system above, for which of the [#permalink]

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New post 04 May 2014, 02:05
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
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New post 04 May 2014, 02:14
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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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Re: In the rectangular coordinate system above, for which of the [#permalink]

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New post 21 Jul 2014, 09:54
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
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Re: In the rectangular coordinate system above, for which of the [#permalink]

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New post 21 Jul 2014, 10:30
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


Image
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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New post 21 Jul 2014, 12:07
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.
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New post 21 Jul 2014, 12:08
also how is the height 1 for S?
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New post 21 Jul 2014, 12:12
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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