AB is a tangent to a circle whose radius is 10 cm.  The area shaded portion is:

(50 - \(\frac{25}{2}\) \(\pi \)) sq. cm

ΔAOB is an isosceles right angle triangle of side OA = AB = 10 cm

Area of shaded region = area of Δ AOB - area of sector

                                    = \(\frac{1}{2}\) × 10 × 10 - \(\pi \) (10)² \(\frac{45°}{360°}\)

                                   = (50 - \(\frac{25}{2}\) \(\pi \)) sq. cm