Question

What is the area of the largest triangle that can be inscribed in a semicircle whose radius is $r$ cm?

• A. $2rc{m}^2$
• B. $r^{2}c{m}^2$
• C. $2r^{2}c{m}^2$
• D. $\frac{r}{2}c{m}^2$

Answer 1

The correct option is D $\frac{r}{2}c{m}^2$

The largest triangle inscribed in a semi-circle have base height equals to diameter of semi-circle and height equals to radius.

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

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