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

Question

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

Bunuel · Accepted Answer

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.

b2bt · Answer

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

madn800 · Answer

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.

WoundedTiger · Answer

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

Senthil1981 · Answer

The figure can be seen as four identical squares with identical shaded region and each individual square. And the shaded region is from one end to the mid point of the other corner. This means it's 1/4 of the area of the main square. Since these are identical, the Answer is B) 1/4

Hero8888 · Answer

Since the answer choices are quite far from one another, the best way for such graphical problems is approximation.
We have got 4 right triangles, which you can easily fit into one of the small triangle (1/4 of original one). Hence the ratio is 1:4. Time taken 47 sec.

GMATinsight · Answer

In such question Most important part is to break the shaded portion into a few recognizable figures like I have broken as shown in figure attached

Answer: Option B

GMATinsight · Answer

Adding Video solution to the thread.

Answer: Option B

https://www.youtube.com/watch?v=olcaBBpqrzI

CEdward · Answer

Am I guilty? It is easily recognizable that the shaded region makes up 1/4 of the square. Each smaller triangle makes up 1/4 of 1/4 of the square.

Is there a better analysis?

bumpbot · Answer

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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

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