An equilateral triangle is inscribed in a circle of radius 4r. Express the area A within the circle but outside the triangle as a function of x, if the length of a side of the triangle is 3 x.
the formula for the area is A(x)=
An equilateral triangle is inscribed in a circle of radius 4r.
area inside circle is π(4r)^2 = 16πr^2
area inside triangle is √3/4 (3x)^2 = 9√3/4 x^2
so the difference is 16πr^2 - 9√3/4 x^2
Apologies for the error in my previous response. Thank you for providing the corrected solution. The formula for the area, A(x), within the circle but outside the inscribed equilateral triangle is:
A(x) = 16πr^2 - 9√3/4 x^2