Question

The area in ( $c{m}^2$) of the largest triangle that can be inscribed in a semicircle of radius r cm is

• A. $\frac{1}{3}\pi r^2$
• B. $2r^2$
• C. $r^2$
• D. $\frac{1}{2}\pi r^2$

Answer 1

Answer: (C)

$r^2$

The largest triangle inscribed in a semicircle has a height = radius of the circle

base = diameter of the circle

$\therefore$ Area of a triangle $=\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times 2r\times r=r^2$

Hence, option C is correct.