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