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# What is the area of the shaded region in the circle above?

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Math Expert
Joined: 02 Sep 2009
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What is the area of the shaded region in the circle above?  [#permalink]

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30 Aug 2018, 05:16
00:00

Difficulty:

25% (medium)

Question Stats:

90% (00:41) correct 10% (00:54) wrong based on 34 sessions

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What is the area of the shaded region in the circle above?

(1) The radii shown are 60 degrees apart.
(2) The radius of the circle is 2.

Attachment:

image019 (1).jpg [ 2.03 KiB | Viewed 471 times ]

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Re: What is the area of the shaded region in the circle above?  [#permalink]

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30 Aug 2018, 05:24
1
Bunuel wrote:

What is the area of the shaded region in the circle above?

(1) The radii shown are 60 degrees apart.
(2) The radius of the circle is 2.

Attachment:
image019 (1).jpg
Shaded area - - - > area of sector - area of triangle

Minimum info needed is angle of Arc and radius

St1) just tells that triangle is equilateral (60-60-60---> both radius gives equal angle)

Not sufficient

St2) gives radius but not central angle

Combining
We have both required. Don't calculate. Be assure that you know the answer can be derived.

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Re: What is the area of the shaded region in the circle above?  [#permalink]

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30 Aug 2018, 05:27
Bunuel wrote:

What is the area of the shaded region in the circle above?

(1) The radii shown are 60 degrees apart.
(2) The radius of the circle is 2.

Attachment:
image019 (1).jpg

PLAN: Area of the shaded region = Area of sector - Area of the unshaded triangle in the sector

Also, Area of Sector = (angle/360)*2πr

Question : Area of the shaded region = ?

Statement 1: The radii shown are 60 degrees apart

This gives us only the angle at the centre which also ensures that other two angles of unshaded triangle are 60º (as other two sides are equal to radius) but it doesn't give us the length of radius hence

NOT SUFFICIENT

Statement 2: The radius of the circle is 2

Now, we know the radius but we don't know the angle at the centre of the sector hence

NOT SUFFICIENT

COmbining the two statements

Area of sector = (60/360)*2π*2 = (2/3)π
Area of the unshaded triangle = (√3/4)*2^2 = √3

Hence area of the shaded region = (2/3)π - √3

SUFFICIENT

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Re: What is the area of the shaded region in the circle above?   [#permalink] 30 Aug 2018, 05:27
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