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In the figure given below, ABCD is a square, and P, Q, R and

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In the figure given below, ABCD is a square, and P, Q, R and [#permalink] New post 03 Oct 2013, 01:12
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Attachment:
tS6VTJ2.jpg
tS6VTJ2.jpg [ 11.04 KiB | Viewed 1190 times ]

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8
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Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink] New post 03 Oct 2013, 01:27
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b2bt wrote:
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The attachment tS6VTJ2.jpg is no longer available

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8


Attachment:
Untitled.png
Untitled.png [ 30.11 KiB | Viewed 1178 times ]

Consider square APNS and say its side is 1. In this case:

The area of APNS is 1.
MN = 1/2, which means that the area of SMN is 1/2*1/2*1=1/4.

(shaded)/(square)=(1/4)/1=1/4.

The ratio for the entire square would be the same.

Answer: B.
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Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink] New post 03 Oct 2013, 02:08
Bunuel wrote:
b2bt wrote:
Attachment:
tS6VTJ2.jpg

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8


Attachment:
Untitled.png

Consider square APNS and say its side is 1. In this case:

The area of APNS is 1.
MN = 1/2, which means that the area of SMN is 1/2*1/2*1=1/4.

(shaded)/(square)=(1/4)/1=1/4.

The ratio for the entire square would be the same.

Answer: B.



How did you get MN as half? I solved the same way but assumed it to half...
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Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink] New post 18 Nov 2013, 18:39
APNS is a square. It's side is 1(as assumed by buneul). This means that ABQS is a rectangle with AS=1 and SQ=2. Hence, PN=1. SB and AQ are diagonals of the rectangle. Let them meet at the point M. Draw an imaginary line say XY passing through M and parallel to both AB and SQ. Now observe that PN bisects SQ that is SN=NQ=1. This implies that XY passing through M should also bisect AS, PN and BQ. Therefore, MN=1/2. This property holds good for all rectangles.
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Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink] New post 19 Nov 2013, 03:17
b2bt wrote:
Bunuel wrote:
b2bt wrote:
Attachment:
tS6VTJ2.jpg

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8


Attachment:
Untitled.png

Consider square APNS and say its side is 1. In this case:

The area of APNS is 1.
MN = 1/2, which means that the area of SMN is 1/2*1/2*1=1/4.


(shaded)/(square)=(1/4)/1=1/4.

The ratio for the entire square would be the same.

Answer: B.



How did you get MN as half? I solved the same way but assumed it to half...



Hello B2bt,

Consider triangle SMN and SBQ

Angles S is common
Angle N is equal to Angle Q and
Angle M is equal to angle B

Since the triangles are similar therefore MN=1/2BQ ie. 1/2
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Re: In the figure given below, ABCD is a square, and P, Q, R and   [#permalink] 19 Nov 2013, 03:17
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