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In the figure above, the quarter circle with center D has a radius of
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02 Feb 2022, 06:30
02 Feb 2022, 06:30
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62% (01:58) correct
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In the figure above, the quarter circle with center D has a radius of 4 and rectangle ABCD has a perimeter of 20. What is the perimeter of the shaded region?
A \(20 - 8\pi\)
B \(10 + 2\pi\)
C \(12 + 2\pi\)
D \(12 + 4\pi\)
E \(4 + 8\pi\)
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2932
Given Kudos: 1277
GPA: 3.39
Re: In the figure above, the quarter circle with center D has a radius of
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13 Feb 2022, 07:03
13 Feb 2022, 07:03
1
Expert Reply
The perimeter ABCE = AB + BC + EC + AE
From the question stem we know:
white area is a quarter of a circle with center D.
radius = 4 = DC = ED
1) Lets find EC, which will be 1/4th of the circumference of the circle.
Circumference = 2πr = 8π
EC = 8π *1/4 = 2π
2) Find BC.
We know CD = radius = 4 = AB
We know the perimeter is 20.
Perimeter = 2CD + 2BC
20 = 2*4 + 2BC
BC = 6
3) Lets plug in our values and determine the answer.
ABCE = AB + BC + EC + AE
AB = 4
BC = 6
EC = 2π
AE = ?
ABCE = 10 + 2π + AE
Only option is C since we know AE>0.
==> C
From the question stem we know:
white area is a quarter of a circle with center D.
radius = 4 = DC = ED
1) Lets find EC, which will be 1/4th of the circumference of the circle.
Circumference = 2πr = 8π
EC = 8π *1/4 = 2π
2) Find BC.
We know CD = radius = 4 = AB
We know the perimeter is 20.
Perimeter = 2CD + 2BC
20 = 2*4 + 2BC
BC = 6
3) Lets plug in our values and determine the answer.
ABCE = AB + BC + EC + AE
AB = 4
BC = 6
EC = 2π
AE = ?
ABCE = 10 + 2π + AE
Only option is C since we know AE>0.
==> C
Re: In the figure above, the quarter circle with center D has a radius of
[#permalink]
29 Apr 2024, 15:55
29 Apr 2024, 15:55
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