Area of triangle

Area of the brown triangle is

$A_{\triangle}=\dfrac{25}{4}\sqrt3$

Area of the original inscribed equilateral triangle (green and brown) is

$A=6A_{\triangle}=\dfrac{75}{4}\sqrt3\approx\boxed{32.476}$

we know that "R = abc/4*area" where R is circumradius & a,b,c are sides of the triangle.

since it is an equilateral triangle, we can say a=b=c & area = [root(3)*a^2]/4. Also given R = 5.

using the formula and the given facts, v can solve to get a=b=c=5*root(3)

then calculate area to find the correct answer

Three congruent obtuse triangles combine to form the equilateral triangle with circumscribing circle radius 5; the area of the equilateral triangle is 3(2.5√3)(2.5)