Question

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is
(a)​ r² sq. units (b) $\frac{1}{2}$ r² sq. units (c) 2 r² sq. units (d) $\sqrt{2}$ r² sq. units

Answer 1

Area of a triangle = $\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$
$\Rightarrow Area=\frac{1}{2}\times \left(2r\right)\times r=r^2$
So, the area of the largest triangle that can be inscribed in a semi-circle of radius r is r²
Hence, the correct answer is option (a).