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# In the figure above, if semicircular arc AB has length 6π, and semicir

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Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135880 [0], given: 12715

In the figure above, if semicircular arc AB has length 6π, and semicir [#permalink]

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23 Nov 2017, 00:14
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Question Stats:

70% (00:28) correct 30% (00:22) wrong based on 9 sessions

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In the figure above, if semicircular arc AB has length 6π, and semicircular arc BC has length 4π, what is the area of rectangle ABCD?

(A) 96
(B) 48
(C) 16√6
(D) 24
(E) 6

[Reveal] Spoiler:
Attachment:

2017-11-22_1024.png [ 4.58 KiB | Viewed 257 times ]
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135880 [0], given: 12715

VP
Joined: 22 May 2016
Posts: 1136

Kudos [?]: 407 [0], given: 647

In the figure above, if semicircular arc AB has length 6π, and semicir [#permalink]

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23 Nov 2017, 12:48
Bunuel wrote:

In the figure above, if semicircular arc AB has length 6π, and semicircular arc BC has length 4π, what is the area of rectangle ABCD?

(A) 96
(B) 48
(C) 16√6
(D) 24
(E) 6

[Reveal] Spoiler:
Attachment:
2017-11-22_1024.png

The diameter of each semi-circle = one side of the rectangle

The circumference of a semi-circle = $$\frac{πd}{2}$$

Arc AB has length $$6π$$
$$6π =\frac{πd}{2}$$
$$d = 12$$ = side AB = length of rectangle ABCD

Arc BC has length $$4π$$
$$4π =\frac{πd}{2}$$
$$d = 8$$ = side BC = width of rectangle

Rectangle area = L*W =
$$(12*8) = 96$$

Kudos [?]: 407 [0], given: 647

In the figure above, if semicircular arc AB has length 6π, and semicir   [#permalink] 23 Nov 2017, 12:48
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