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In the rectangular coordinate system above, for which of the
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Updated on: 21 Jul 2014, 11:25
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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 Attachment:
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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.
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In the rectangular coordinate system above, for which of the
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22 Nov 2010, 07:56
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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Re: In the rectangular coordinate system above, for which of the
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04 May 2014, 03:14
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
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20 Oct 2011, 22:26
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
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19 Jul 2019, 19:00
People can be confused over R. Use a right triangle to articulate side length of square R as per my diagram.
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Re: In the rectangular coordinate system above, for which of the
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06 Mar 2014, 02:34
Bumping for review and further discussion.GEOMETRY: Shaded Region Problems!
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Re: In the rectangular coordinate system above, for which of the
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04 May 2014, 03:05
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
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21 Jul 2014, 10:54
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
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21 Jul 2014, 11:30
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
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21 Jul 2014, 13:07
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
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21 Jul 2014, 13:08
also how is the height 1 for S?



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Re: In the rectangular coordinate system above, for which of the
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21 Jul 2014, 13:12
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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Re: In the rectangular coordinate system above, for which of the
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24 Jan 2017, 07:35
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 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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Re: In the rectangular coordinate system above, for which of the
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25 Jun 2019, 01:57
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?




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