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

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Joined: 02 Sep 2009
Posts: 50075
In the figure above, if semicircular arc AB has length 6π, and semicir  [#permalink]

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23 Nov 2017, 01:14
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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

Attachment:

2017-11-22_1024.png [ 4.58 KiB | Viewed 483 times ]

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

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23 Nov 2017, 13:48
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

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 =
$$(12*8) = 96$$

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In the figure above, if semicircular arc AB has length 6π, and semicir &nbs [#permalink] 23 Nov 2017, 13:48
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