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66% (01:11) correct
33% (01:03) wrong based on 3 sessions
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In the figure below, ABCD is a rectangle, and BE and CF are arcs of circles centered at A and D. What is the area of the striped region?
A. \(10 – π\)
B. \(2(5 – π)\)
C. \(2(5 – 2π)\)
D. \(6 + 2π\)
E. \(5(2 – π)\)
Attachment:
1.jpg [ 16.21 KiB | Viewed 558 times ]
Posts: 16,401
OE
The entire region is a 2 × 5 rectangle whose area is 10. Since the white region consists of two quarter-circles of radius 2, the total white area is that of a semicircle of radius \(2:\frac{1}{2} π(2)^2=2 π\). Therefore, the area of the striped region is \(10 – 2π = 2(5 – π), B.\)
The entire region is a 2 × 5 rectangle whose area is 10. Since the white region consists of two quarter-circles of radius 2, the total white area is that of a semicircle of radius \(2:\frac{1}{2} π(2)^2=2 π\). Therefore, the area of the striped region is \(10 – 2π = 2(5 – π), B.\)
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