Circle with known radius within a triangle, find dimension of triangle.?

Question

we have a circle with the radius of 3.15 cm and an unknown triangle. using the circle, find the dimension of the smallest possible triangle that would fit the circle.

Answer 1

I assume you mean, the smallest possible triangle that would fit around the outside of the circle. This is a triangle with an incircle. The smallest such triangle would be equilateral.

Let
r = radius incircle
h = height equilateral triangle
s = length side of triangle
A = area triangle

r = h/3
h = 3r

s = (2/√3)h = (2/√3)(3r) = (2√3)r

A = (1/2)sh = (1/2)[(2√3)r](3r) = (3√3)r²
A = (3√3)(3.15)² ≈ 51.56 cm²