2. The perimeter of parallelogram $A B C D$ is 75 cm, and when $B C$ is the base, the height is 14 cm (as shown in the figure);

when $C D$ is the base, the height is 16 cm, find: the area of parallelogram $A B C D$.
2. 280
2.【Solution】The area of a parallelogram $=$ base $\times$ height, so: $\mathrm{BC} \times 14=\mathrm{CD} \times 16$.

Thus $\mathrm{BC}: \mathrm{CD}=16: 14, \quad \mathrm{BC}=\frac{75}{2} \times \frac{16}{14+16}, \quad S_{A B C D}=14 \times \frac{75}{2} \times \frac{16}{14+16}=$ 280 (square centimeters)
Therefore, the area of parallelogram $\mathrm{ABCD}$ is 280 square centimeters