The perimeter of a certain sector of a circle of radius $\displaystyle 5.6$ m is $\displaystyle 20.0$ m. Find the area of the sector.

\[\begin{aligned} & 2 r+\frac{2 \pi r \theta}{360}=20 \\ & \Rightarrow 11.2+2 \times \frac{22}{7} \times 5.6 \times \frac{\theta}{360}=20 \end{aligned} \] Solving, we get \(\displaystyle \theta=90^{\circ}\) \[\begin{aligned} & \therefore \text { Area of sector }=\frac{22}{7} \times 5.6 \times 5.6 \times \frac{90}{360} \\ & \quad=24.64 \mathrm{~m}^{2} \end{aligned} \]