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The side of a square has the length of 8. What is the area o

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by Max@Math Revolution » Sun Jun 26, 2016 5:26 pm
The side of a square has the length of 8. What is the area of the region shaded?
A. 48-8Ï€
B. 48-6 π
C. 24+6Ï€
D. 16+8Ï€
E. 64-8Ï€

*An answer will be posted in 2 days.
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by 800_or_bust » Sun Jun 26, 2016 6:37 pm
Max@Math Revolution wrote:The side of a square has the length of 8. What is the area of the region shaded?
A. 48-8Ï€
B. 48-6 π
C. 24+6Ï€
D. 16+8Ï€
E. 64-8Ï€

*An answer will be posted in 2 days.
I'm assuming both of those are semicircles of diameter equal to 8. Hard to tell from the drawing alone. If so, they should intersect right in the middle of the square, so we can draw a smaller square in the far bottom left corner with sides of 4 (the radii of the circle). This square has area of 16. The remaining circular region (consisting of two quarter-circles of radius 4, or collectively one semi-circle) has area equal to 8Ï€ (Ï€(4^2)/2). The total area of the square is 8x8 = 64. Thus, the area of the shaded region is 48-8Ï€.
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by Max@Math Revolution » Tue Jun 28, 2016 5:26 pm
The area of a square whose side is 8 - (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded
The correct answer is A.
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