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# The diameters of the semicircles above are 8, and the diamet

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The diameters of the semicircles above are 8, and the diamet [#permalink]  04 Oct 2020, 09:07
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Question Stats:

90% (02:13) correct 9% (02:41) wrong based on 11 sessions
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GRE The diameters of the semicircles above are 8.png [ 22.73 KiB | Viewed 198 times ]

The diameters of the semicircles above are 8, and the diameter of the semicircle on the right is perpendicular to those of the other two semicircles. What is the total area of the shaded region?

A. 12π + 64

B. 24π + 12

C. 24π + 48

D. 32π + 48

E. 32π + 64
[Reveal] Spoiler: OA

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Re: The diameters of the semicircles above are 8, and the diamet [#permalink]  04 Oct 2020, 19:54
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area of three semi circles =24π (each 8π)

area of three triangles =48 (each will be 16)

total area of shaded region =24π+48

option C is correct
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Re: The diameters of the semicircles above are 8, and the diamet [#permalink]  04 Oct 2020, 23:35
First

Find the area of 3 semicircle = 24π
then find the area of square =8*8 =64
divide it by 4 since they are 4 equal triangles in that square
we get 16
Subtract 16 from 64 we get 48
Finally add area of 3 semicircle + area of the remaining portion of square
we get 48+24π.
Re: The diameters of the semicircles above are 8, and the diamet   [#permalink] 04 Oct 2020, 23:35
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