O is the center of a circle with AC = 24 cm, AB = 7 cm, ∠BOD = 90°.  The area of shaded region is:

284.295 sq. cm

Area of shaded region I = Area of semi circle - Area of Δ ABC

BC² = AC² + AB² = 7² + 24² = 25 c.m.

⇒ Area of region I  = \(\frac{1}{2}\)\(\pi \)r² - \(\frac{1}{2}\) AC × AB

                          = \(\frac{22}{7}\) × \(\frac{1}{2}\) × \(\frac{25}{2}\) × \(\frac{25}{2}\) -  \(\frac{1}{2}\) × 24 × 7

= 245.53 - 84 = 161.535

⇒ Area of region II = area of quadrant BOD = \(\frac{1}{4}\) \(\pi \)r²

= \(\frac{1}{4}\) × \(\frac{22}{7}\) × \(\frac{25}{2}\) × \(\frac{25}{2}\) = 122.76

Total area = 161.535 + 122.76 = 284.295 cm²