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# Each of the three shaded regions above is a semicircle. If AB = 4, CD

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Math Expert
Joined: 02 Sep 2009
Posts: 55668
Each of the three shaded regions above is a semicircle. If AB = 4, CD  [#permalink]

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11 Jan 2019, 01:20
00:00

Difficulty:

45% (medium)

Question Stats:

50% (01:18) correct 50% (01:17) wrong based on 17 sessions

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Each of the three shaded regions above is a semicircle. If AB = 4, CD = 2BC, and BC = 2AB, then the area of the entire shaded figure is

A. 28π
B. 42π
C. 84π
D. 96π
E. 168π

Attachment:

2019-01-11_1218.png [ 12.32 KiB | Viewed 293 times ]

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Re: Each of the three shaded regions above is a semicircle. If AB = 4, CD  [#permalink]

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11 Jan 2019, 01:33
Bunuel wrote:

Each of the three shaded regions above is a semicircle. If AB = 4, CD = 2BC, and BC = 2AB, then the area of the entire shaded figure is

A. 28π
B. 42π
C. 84π
D. 96π
E. 168π

Attachment:
The attachment 2019-01-11_1218.png is no longer available

IMO: B
Solution Attached

Cheers!
Shantanu Sharma
MBA and Beyond Consulting
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Re: Each of the three shaded regions above is a semicircle. If AB = 4, CD  [#permalink]

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11 Jan 2019, 03:19
Bunuel wrote:

Each of the three shaded regions above is a semicircle. If AB = 4, CD = 2BC, and BC = 2AB, then the area of the entire shaded figure is

A. 28π
B. 42π
C. 84π
D. 96π
E. 168π

Attachment:
2019-01-11_1218.png

DIAMETER
AB= 4 ; CD=16 ; BC = 8
radius ab= 2; cd=8 ; bc= 4

so area of semicircle ab,bc,cd = pi/2 * ( 4^2+8^2+2^2)
= 42 pi
IMO B
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Re: Each of the three shaded regions above is a semicircle. If AB = 4, CD   [#permalink] 11 Jan 2019, 03:19
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