$\mathrm{AQ}: \mathrm{QB}=2: 3$ হলে,$\triangle \mathrm{PQB}$ এর ক্ষেত্রফল নির্ণয় কর।

সমাধান: $Q \equiv\left(\frac{2 \times 0+3 \times 3}{2+3}, \frac{2 \times 2+3 \times 0}{2+3}\right)$$=\left(\frac{9}{5}, \frac{4}{5}\right)$

$\triangle \mathrm{PQB}$ এর ক্ষেত্রফল,

$\begin{array}{l} =\frac{1}{2}\left|\left(3-\frac{9}{5}\right)\left(\frac{4}{5}-2\right)-\left(\sqrt{3}-\frac{4}{5}\right)\left(\frac{9}{5}-0\right)\right| \\ =\frac{1}{2}\left|\left(\frac{6}{5}\right)\left(-\frac{6}{5}\right)-\frac{9 \sqrt{3}}{5}+\frac{36}{25}\right| \\ =\frac{1}{2}\left|-\frac{36}{25}-\frac{9 \sqrt{3}}{5}+\frac{36}{25}\right| \\ =\frac{9 \sqrt{3}}{10} \text { বর্গ একক। } \end{array}$