In the given figure find the area of the shaded region if ac = 24 cm ab = 7cm and o is the centre

See the attached figure to better understand the problem

we know that

The inscribed angle in a circle measures half of the arc it comprises.

in this problem
the inscribed angle= ∠ACB
and the arc it comprises measures 180°
then
the ∠ACB=180°/2-------> ∠ACB=90°

applying the Pythagorean theorem
AC²+CB²=AB²-------> AB²=24²+7²-------> AB²=625------> AB=25 cm

the diameter of circle is AB
radius=25/2--------> r=12.5 cm

[the area of a half circle]=pi*r²/2------> pi*12.5²/2--------> 245.44 cm²

[area of triangle ABC]=AC*CB/2--------> 24*7/2-------> 84 cm²

[the area of the shaded region]=[the area of a half circle]-[area of triangle ABC]

[the area of the shaded region]=245.44-84-------> 161.44 cm²

the answer is 
the area of the shaded region is 161.44 cm²

(1/x + 1)^2 + 6 (1/x + 1) +5