Question

what is the area of the triangle inscribed in a semicircle? ​

Answer 1

Answer:

The area of any triangle is given by (base)*( height)/2. Thus, the triangle of maximum area inscribed in a semicircle, the base being fixed, will be the triangle of maximum height. The height is given by r * sin (Theta), maximum when Theta = Pi / 2. The triangle then has height r, base 2r and area r ^ 2.