See the attached figure to better understand the problem
we know that
<span>The inscribed angle in a circle measures half of the arc it comprises.
</span>in this problem
the inscribed angle= ∠ACB
and the arc it comprises measures 180°
then
the ∠ACB=180°/2-------> ∠ACB=90°
<span>applying the Pythagorean theorem
</span>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
we know that
<span>The inscribed angle in a circle measures half of the arc it comprises.
</span>in this problem
the inscribed angle= ∠ACB
and the arc it comprises measures 180°
then
the ∠ACB=180°/2-------> ∠ACB=90°
<span>applying the Pythagorean theorem
</span>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
