The area of the largest triangle that can be inscribed in a semi-circle of radius 6 cm is:

36 cm²

We know that,

Area of triangle = \(\frac{1}{2}\) × Base × Height

Radius of semi-circle = 6 cm

So,

The largest triangle that can be inscribed in a semi-circle will have a base equal to the diameter and a height equal to the radius of the semi-circle.

Base = 2 × 6 = 12 cm

Height = R = 6 cm

Area of the triangle = \(\frac{1}{2}\) × 12 × 6

= 6 × 6 = 36 cm²