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# Given a rectangle and circle that share a center with a vertex of a tr

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Math Expert
Joined: 02 Sep 2009
Posts: 55653
Given a rectangle and circle that share a center with a vertex of a tr  [#permalink]

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11 Sep 2018, 03:11
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Question Stats:

86% (01:38) correct 14% (01:16) wrong based on 9 sessions

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Given a rectangle and circle that share a center with a vertex of a triangle as shown above, what is the area of the shaded region?

(1) The area of the inscribed rectangle is 4.
(2) The rectangle shown is a square.

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image016.jpg [ 2.22 KiB | Viewed 337 times ]

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Re: Given a rectangle and circle that share a center with a vertex of a tr  [#permalink]

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11 Sep 2018, 04:13
Bunuel wrote:

Given a rectangle and circle that share a center with a vertex of a triangle as shown above, what is the area of the shaded region?

(1) The area of the inscribed rectangle is 4.
(2) The rectangle shown is a square.

Attachment:
image016.jpg

ARea of the shaded region can be calculated in two ways
1) (Area of Circle-Area of square (if it's a square))/4
2) Area of sector - Area of triangle adjacent to the shaded area

Question : Area of the shaded region = ?

Statement 1: The area of the inscribed rectangle is 4
Since we don't know whether the rectangle is square or not also we don't know the area of circle hence

NOT SUFFICIENT

Statement 2: The rectangle shown is a square.
But the measure of any dimension or area is unknown hence

NOT SUFFICIENT

Combining the two statements
Square with area 4 will have dimension of side as 2 and diagonal (i.e. diameter of circle) 2√2 hence
we can calculate area of circle π(2√2)^2 and also area of shaded region = [π(2√2)^2 - 4]/4
SUFFICIENT

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Re: Given a rectangle and circle that share a center with a vertex of a tr   [#permalink] 11 Sep 2018, 04:13
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