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 =

\((12*8) = 96\)

Answer A

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