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# What is the area of the region of diagram?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8787
GMAT 1: 760 Q51 V42
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What is the area of the region of diagram?  [#permalink]

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02 May 2016, 22:28
1
00:00

Difficulty:

25% (medium)

Question Stats:

85% (02:25) correct 15% (02:40) wrong based on 41 sessions

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What is the area of the region of diagram?

A. 8+(3π/2)
B. 10+(3π/2)
C. 8+3π
D. 10+3π
E. 8+6π

* A solution will be posted in two days.

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4.png [ 16.66 KiB | Viewed 1066 times ]

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Marshall & McDonough Moderator
Joined: 13 Apr 2015
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Location: India
Re: What is the area of the region of diagram?  [#permalink]

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03 May 2016, 11:13
Area of rectangular region (shaded portion in the attachment) = 4 * 2 + 1 * 2 = 10
Area of semi-circular region = 3*(pi*1^2)/2 = 1.5pi

Total area = 10 + 1.5pi

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IMG_20160504_003643.jpg [ 1.82 MiB | Viewed 1033 times ]

Manager
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Re: What is the area of the region of diagram?  [#permalink]

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03 May 2016, 12:14
In this digram you have:

3 semi circles : 3/2 * Pi * R², with R=1

1 rectangle : 4*2

1 square : 1* 2

Sum = 3/2 Pi + 10
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8787
GMAT 1: 760 Q51 V42
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What is the area of the region of diagram?  [#permalink]

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08 May 2016, 17:53
As you can see from the figure attached, we have a rectangle that has an area of 4*2=8 and 2*1=2. Also, there are three semicircles with 1 as their radii. All together, the area is 8+2+3(π/2)= 10+(3π/2). Hence, B is the correct answer.
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.png [ 12.54 KiB | Viewed 938 times ]

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What is the area of the region of diagram?   [#permalink] 08 May 2016, 17:53
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