Question

maximum area of a triangle inscribed in a semi circle of radius r

Answer 1

The radius of the semicircle = height of the triangle
The diameter of the circle = Base of the triangle

Therefore maximum area of the triangle = 1/2 × bh
= 1/2 × r ×2r
=r^2

Answer 2

Abc is the triangle
OB and OC are radii . So the are of r units
Area of triangle =1/2 *base*height
=1/2*2(OB)*OC
=1/2 * 2r*r
=r square is the answer