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Find the area of the shaded region

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  • #1
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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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First, notice that the problem has lots of symmetry, so you might be able to save some work at some point. Now, the distances [itex]\|AB\|, \ \|AC\|, \ \|BC\|[/itex] 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?
 

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