SOLUTION: Triangle ABC is an equilateral triangle with sides of length 3 cm. AB, AC, and BC are arcs of circles having their centres at C, B, and A respectively. Find the total area of the n

Question 1101878: Triangle ABC is an equilateral triangle with sides of length 3 cm. AB, AC, and BC are arcs of circles having their centres at C, B, and A respectively. Find the total area of the non-shaded region (the area of the triangle itself, not including the arcs), in cm^2.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

If the drawing above is what the figure is supposed to look like,
the arcs have a radius of .
Each angle in an equilateral triangle is
or of a whole turn,
so the total area of the 3 circle sectors
is half a circle of radius ,
or

.
The area of an equilateral triangle can be calculated as
,
so the area of the whole triangle in the problem is

.
The area of the triangle minus the 3 sectors is

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