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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
In the figure shown, ABCD is a square with side length 5 sqrt 2. Two q
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17 Aug 2021, 09:10
17 Aug 2021, 09:10
Expert Reply
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Question Stats:
57% (02:55) correct
42% (02:45) wrong based on 14 sessions
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In the figure shown, ABCD is a square with a side length of 5 sqrt 2. Two quarter-circles BED and DFB are centered at A and C, respectively. What is the area of the shaded region?
A. 50pi-25
B. 25pi−50
C. 50pi/3
D. 25pi/3
E. 25pi
Re: In the figure shown, ABCD is a square with side length 5 sqrt 2. Two q
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20 Aug 2021, 15:45
20 Aug 2021, 15:45
1
The two unshaded portions in the figure are of the same area (as there is a symmetry). Let's see each of them is "A". And the shaded area= "B"
So, 2A+B= area of square = (5 sqrt 2)^2 = 50
And A+B= area of a quarter circle = 1/4 * pi * (5 sqrt 2)^2 = 50*pi/4
So, A= 50 - 50*pi/4 = (200-50*pi)/4
And unshaded region = 25*pi - 50
So, 2A+B= area of square = (5 sqrt 2)^2 = 50
And A+B= area of a quarter circle = 1/4 * pi * (5 sqrt 2)^2 = 50*pi/4
So, A= 50 - 50*pi/4 = (200-50*pi)/4
And unshaded region = 25*pi - 50
Re: In the figure shown, ABCD is a square with side length 5 sqrt 2. Two q
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07 Dec 2021, 22:50
07 Dec 2021, 22:50
1
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