Area of a crescent

[BMAD]

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?

[kevink2]

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

Or

pi/8 - pi/8 + 1/4

So 1/4

Edited December 16, 2013 by kevink2