A sector of a circle of radius 8 cm contains an angle of 135°.

We know that the area A of a sector of an angle θ in the circle of radius r is given by

$A=\frac{\theta}{360^{\circ}} \times \pi r^{2}$

It is given that $r=8 \mathrm{~cm}$ and $\theta=135^{\circ}$.

Now we substitute the value of $r$ and $\theta$ in above formula,

$A=\frac{135^{\circ}}{360^{\circ}} \times \pi \times 8 \times 8 \mathrm{~cm}^{2}$

$=24 \pi \mathrm{cm}^{2}$