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In the rectangular coordinate system above, for which of the [#permalink ]
22 Nov 2010, 05:29
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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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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 [#permalink ]
22 Nov 2010, 06:56

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Re: In the rectangular coordinate system above, for which of the [#permalink ]
20 Oct 2011, 21:26

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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Re: In the rectangular coordinate system above, for which of the [#permalink ]
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Re: In the rectangular coordinate system above, for which of the [#permalink ]
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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Re: In the rectangular coordinate system above, for which of the [#permalink ]
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 ]
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 ]
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

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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Re: In the rectangular coordinate system above, for which of the [#permalink ]
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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Re: In the rectangular coordinate system above, for which of the [#permalink ]
21 Jul 2014, 12:08

also how is the height 1 for S?

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Re: In the rectangular coordinate system above, for which of the [#permalink ]
21 Jul 2014, 12:12

Re: In the rectangular coordinate system above, for which of the
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