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Find the area of the Reuleaux triangle given below.  The radius of each circle is 1.

 

 Jun 2, 2020
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The area of the triangle (not counting the circular segments) is:  A  =  sqrt(3)/4·12  =  sqrt(3)/4.

 

Since the triangle is an equilateral triangle, each arc is 60o.

The area of one sector of the circle is one-sixth of the circle:  A  =  (1/6)·pi·12  =  (1/6)·pi

 

If you add three of these together, you get  (1/2)·pi.

 

However, this means that you have counted the area of the triangle 3 times, so you'll need to subtract

two of those triangles:   (1/2)·pi.  -  2·sqrt(3)/4

 Jun 2, 2020

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