Area of a segment

A circular sign has radius 9 cm. A chord cuts off a minor segment. The central angle between the radii to the ends of the chord is $90^\circ$. The area of the triangle formed by these two radii and the chord is $\dfrac{81}{2}$ cm$^2$.

Using area of segment = area of sector − area of triangle, find the exact area of this segment in cm$^2$.