21. The radii of circles $\odot P$, $\odot Q$, and $\odot R$ are $1$, $2$, and $3$, respectively. They are all on the same side of line $l$ and are tangent to $l$, with points of tangency being $P'$, $Q'$, and $R'$, respectively. Additionally, $\odot Q$ is tangent to both $\odot P$ and $\odot R$. Then the area of $\triangle PQR$ is ( ).
(A) 0
(B) $\sqrt{\frac{2}{3}}$
(C) $\sqrt{\frac{3}{2}}$
(D) $\sqrt{6}-\sqrt{2}$
(E) 1
21. D.
$$
\begin{array}{l} 
S_{\triangle P Q R}=S_{\text {grid } P P^{\prime} Q^{\prime} Q}+S_{\text {trapezoid } Q Q^{\prime} R^{\prime} R}-S_{\text {irregular } P P^{\prime} R^{\prime} R} \\
= \frac{1}{2}(1+2) \sqrt{(1+2)^{2}-(2-1)^{2}}+ \\
\frac{1}{2}(2+3) \sqrt{(2+3)^{2}-(3-2)^{2}}- \\
\frac{1}{2}(1+3)(\sqrt{8}+\sqrt{24}) \\
= 3 \sqrt{2}+5 \sqrt{6}-4 \sqrt{2}-4 \sqrt{6}=\sqrt{6}-\sqrt{2} .
\end{array}
$$