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# The two semicircles above both have radii of 7. If AB is tangent to th

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Math Expert
Joined: 02 Sep 2009
Posts: 55732
The two semicircles above both have radii of 7. If AB is tangent to th  [#permalink]

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10 Jan 2019, 02:35
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:00) correct 26% (02:00) wrong based on 23 sessions

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The two semicircles above both have radii of 7. If AB is tangent to the semicircles as shown, what is the shaded area, to the nearest integer?

A. 21
B. 42
C. 49
D. 54
E. 77

Attachment:

2019-01-10_1333.png [ 8.37 KiB | Viewed 416 times ]

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The two semicircles above both have radii of 7. If AB is tangent to th  [#permalink]

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10 Jan 2019, 03:31
1
From the figure = $$(Area of the square/2) - 2*(Area of the Quarter circles of radius 7)$$
Area of the quarter circle =$$(Pi*r^2)/4$$
= $$14*14/2 - 2(Pi*7*7/4)$$

= $$14*7 - ((22/7)*7*7)/2$$
=$$14*7-11*7$$
= $$(14-11)*7$$
=21

Option A is correct
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Re: The two semicircles above both have radii of 7. If AB is tangent to th  [#permalink]

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10 Jan 2019, 06:48
Bunuel wrote:

The two semicircles above both have radii of 7. If AB is tangent to the semicircles as shown, what is the shaded area, to the nearest integer?

A. 21
B. 42
C. 49
D. 54
E. 77

Attachment:
2019-01-10_1333.png

good question

given two semi circles of radius 7 so area of both would be
2 * pi * 49 /2 = 49 pi but since we are interested in finding the shaded area we need to so 49/2 * pi = ~77

area of rectangle 14*7 = 98
shaded region = 98-77 = 21 IMO A
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Re: The two semicircles above both have radii of 7. If AB is tangent to th   [#permalink] 10 Jan 2019, 06:48
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