The blue crescent is made up of a semicircle and a quarter circle (of a larger circle). If the width of the figure (diameter of the semicircle) is 1, what is the area of the crescent?
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Posted 16 December 2013 - 04:24 PM
The radius of the yellow+green circle is sqrt(2)/2. (r^2 = 2/4 = 1/2)
So the the area of the yellow triangle is 1/4 (b*h*1/2)
The area of the yellow + green part is 1/4 of the area of the circle (1/4 * pi * 1/2 = pi/8)
The area of the blue + green areas is half of the area of the circle (1/2 * pi * (1/2)^2 or pi/8)
So the area of the blue part is (blue+green) - (Yellow + green) + yellow
pi/8 - pi/8 + 1/4
Edited by kevink2, 16 December 2013 - 04:33 PM.
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