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

The lengths of the sides of a triangular field (ΔABC) are AB = 60 m, BC = 61 m, and AC = 11 m. If AT is drawn perpendicular from vertex A to side BC, then what is the area of ΔABC?

Find the area of an equilateral triangle whose height (altitude) measures 5√3 cm.