A largest triangle that can be inscribed in a semi-circle of radius r units is the triangle having its base as the diameter of the semi-circle and the two other sides are taken by considering a point C on the circumference of the semi-circle and joining it by the end points of diameter A and B.

∴ ∠ C = 90° (by the properties of circle)

So, ΔABC is right angled triangle with base as diameter AB of the circle and height be CD.

Height of the triangle = r

∴ Area of largest ΔABC = (1/2)× Base × Height = (1/2)× AB × CD

= (1/2)× 2r × r = r² sq. units