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12 May 2021, 04:15
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
83% (01:49) correct
17%
(01:34)
wrong
based on 18
sessions
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Not Attempted Yet
Arcs AC, AB and BC are centered at B, C and A respectively, as shown above. If the area of equilateral triangle ABC is √3, what is the area of the shaded region?
A. \(2\pi-3\sqrt{3}\)
B. \(\sqrt{3} - \pi\)
C. \(3\pi\)
D. \(\sqrt{3}+2\pi\)
E. 3
Attachment:
1.png [ 10.23 KiB | Viewed 1831 times ]
12 May 2021, 04:25
Kudos
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Bunuel
Let's look at this whole shaded region as a group of three equal shaded area
Area of equilateral triangle \(= \frac{√3}{4}Side^2 = √3\)
i.e. Side of equilateral Triangle = 2 = Radius of the arc
Each shaded part = Sector - Triangle \(= (\frac{60}{360})*π2^2 - √3 = \frac{2}{3}π-√3\)
Total shaded area = \(3*(\frac{2}{3}π-√3) = 2π-3√3\)
Answer: Option A
12 May 2021, 05:23
Kudos
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Solution:
Side of the equilateral triangle = 2 units
Area of the sector with central angle 60 degrees=60/360∗π(2)^2
=2/3π
Area of the shaded part=3 such overlapping sectors-3*area of the triangle
=3x(2/3)π - 3√3
=2π - 3√3 (option a)
Devmitra Sen
GMAT SME
Side of the equilateral triangle = 2 units
Area of the sector with central angle 60 degrees=60/360∗π(2)^2
=2/3π
Area of the shaded part=3 such overlapping sectors-3*area of the triangle
=3x(2/3)π - 3√3
=2π - 3√3 (option a)
Devmitra Sen
GMAT SME
