An equilateral triangle is inscribed in a circle of radius 2

An equilateral triangle is inscribed in a circle of radius 2r. Express the area A within the circle but outside the triangle as a function or the length 9x of the side of the triangle. The formula for the area is A(x) =

Solution

area of the circle = pi r^2 = 4*pi*r^2
area of triangle = 1/2 bh
to calculate length of each side of the triangle draw points from 2 of the corners to the centre and these lengths are equal to the radius 2r
use pythagoras to solve length = sqrt (4r^2 +4r^2) = 2sqrt (2)r
then calculate area of triangle =sqrt (2) r * [8r^2 - (sqrt((sqrt8 )r/2))]