In the figure above, ABCD is a square, and P and Q are the centers of

Question

https://gmatclub.com/forum/download/file.php?id=61824 In the figure above, ABCD is a square, and P and Q are the centers of identical semicircles BF and AE, respectively. If DE=EA=AF=FB=1, then what is the perimeter of the shaded region? A. 4+π/2 B. 6 C. 8 D. 6+π E. 6+2π Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS 1.png

sumitkrocks · Answer

Radius of the identical semicircle =r= 1/2 
Perimeter of the shaded figure = 2+2+1+1+2*pi*r =6+pi
D is the answer

asishron29181 · Answer

Given P and Q are centers
DE = EA = AF = FB =1

Radius of the semicircle = 1/2
=0.5
Semi perimeter of the circle = π * radius
π* 0.5

Clearly in the figure we can see two semicircle forming the part of shaded region, perimeter of both = (π * 0.5) * 2
= π 
Perimeter of shaded region = 1+1+2+2+ π = π + 6

IMO D

HarshaBujji · Answer

IMO D

Perimeter of intial square =8,
By cutting the square and replacing semi circles of radius 1/2.

Perimeter = 8-2+2 x Πd/2
As d=1,

So perimeter=6+Π

Ans D

Posted from my mobile device

harshtandel838 · Answer

The perimeter of shaded region will be...
 (Length of BC + CD + DE + AF) + (Circumference of semi circle with center P and Q)

i.e.
 Perimeter = ( 2 + 2 + 1 + 1 ) + ( 2 * pi * r ) 
where r = 1/2;
 Perimeter = 6 + pi

Hence, answer is  D

Posted from my mobile device

dcn1102 · Answer

IMO D .

Area of square is 8 . subtracting FB and AE we get 6. Now adding the perimeter of the inner and outer semicircles i.e circumference of one full circle with radius 1/2 we get the answer as 6 + pi.

kantapong · Answer

Perimeter consists of two parts:
1) DE + DC + CB + AF = 6
2) Two times Perimeter of half-circle with radius 0.5 (F to B and A to E) = 2*pi*r where r = 0.5
Hence, my answer is 6 + pi (D)

In the figure above, ABCD is a square, and P and Q are the centers of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In the figure above, ABCD is a square, and P and Q are the centers of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards