Find the shaded area?

Question

each circle has the radius of 5cm.

http://i38.tinypic.com/t6rwjp.jpg

Answer 1

Draw a triangle connecting the radii of each circle. Noting this is an equilateral triangle with sides 10cm. Thus each corner, and thus each sector of the circle is 60°.

Area of triangle - area of sectors = area of shaded region.

5(10sin60°) - (3)(60°/360°)(pi * 5²) = 4.03136202 cm²

Answer 2

Maybe this is a little simpler.

Start with the area of the same triangle and subtract half the area of one circle. There are 3  60 degree segments or 180 total; half of a circle.

Doing it this way came out to 4.0512 cm squared.