21. What is the maximum area that a triangle with sides \(a, b, c\) can have, given that the sides are within the following limits: \(0 \leqslant a \leqslant 1 \leqslant b \leqslant 2 \leqslant c \leqslant 3\) ?
21. $S=\frac{1}{2} a b \sin \alpha$. Takes the maximum value when $a=1, b=2, \sin \alpha=1$,
$S=\frac{1}{2} \cdot 1 \cdot 2 \cdot 1=1$. Under these conditions, $c=\sqrt{1+4}=\sqrt{5}$, which satisfies the problem's condition ( $2 \leqslant c \leqslant 3$).