Area of the largest triangle that can be inscribed in a semi-circle of radius $r$ is:
$r^2$
$2r^2$
$r^3$
$\dfrac{r^2}{2}$
Step-by-Step Solution
Key Concept: Base of triangle $=$ diameter $= 2r$, maximum height $=$ radius $= r$. Area $= \dfrac{1}{2} \times 2r \times r = r^2$.
Stepwise Solution:
Base $= 2r$, max height $= r$. Area $= \dfrac{1}{2} (2r)(r) = r^2$. [1.0 Mark]
Marking Scheme:
• Identifying max height $r$ and base $2r \Rightarrow$ area $r^2$: 1.0 Mark
Correct Answer: $r^2$