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Helpful Geometry formula sheet:best-geometry-93676.html I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.

Last edited by Bunuel on 21 Jul 2014, 10:25, edited 1 time in total.

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

1

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

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: \(area_P=\frac{1}{2}*4*1=2\); \(area_Q=1*2=2\); \(area_R=\frac{2^2}{2}=2\); \(area_S=\frac{1}{2}*3*1=1.5\).

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

1

This post was BOOKMARKED

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

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

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

1

This post received KUDOS

Expert's post

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 \(area_{rhombus}=\frac{d_1*d_2}{2}\). _________________

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?

Re: In the rectangular coordinate system above, for which of the [#permalink]
21 Jul 2014, 10:30

Expert's post

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).

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.

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

Expert's post

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, ...

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