Homework Help: Find the area of the shaded region

1. Apr 29, 2005

fork

In the figure, A, B and C are the centres of three equal circles, each of radius 1 cm. Find the area of the shaded region.

I feel stump with this question. Thanks

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2. Apr 29, 2005

Data

First, notice that the problem has lots of symmetry, so you might be able to save some work at some point. Now, the distances $\|AB\|, \ \|AC\|, \ \|BC\|$ are all 1cm (see why?). Can you construct any triangles that you can find the areas of? Can you construct any circular arcs that you can find the areas of?