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

Algebra ->  Triangles -> 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      Log On


   

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) About Me  (Show Source):
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If the drawing above is what the figure is supposed to look like,
the arcs have a radius of r=3cm%2F2=1.5cm .
Each angle in an equilateral triangle is
60%5Eo or 1%2F6 of a whole turn,
so the total area of the 3 circle sectors
is half a circle of radius 1.5cm ,
or pi%2A1.5%5E2%2F2cm%5E2=1.125picm%5E2 .
The area of an equilateral triangle can be calculated as
sqrt%283%29side%5E2%2F4 ,
so the area of the whole triangle in the problem is
sqrt%283%29%283cm%29%5E2%2F4=2.25sqrt%283%29cm .
The area of the triangle minus the 3 sectors is
2.25sqrt%283%29-1.125picm%5E2=approximately0.3627cm%5E2