The perimeter of the quadrant of a circle is 25 cm.

Let the radius of the circle be r

Now, Perimeter of quadrant $=\frac{1}{4}(2 \pi r)+2 r$

$\Rightarrow 25=\frac{1}{2} \times \frac{22}{7} \times r+2 r$

$\Rightarrow 25=\frac{25 r}{7}$

$\Rightarrow r=7 \mathrm{~cm}$

Area of quadrant $=\frac{1}{4} \pi r^{2}=\frac{1}{4} \times \frac{22}{7} \times 7 \times 7=38.5 \mathrm{~cm}^{2}$

Hence, the area of quadrant is 38.5 cm2