Answer:
Area of the shaded region = 450.52 square inch
Step-by-step explanation:
Area of the shaded region = Area of the circle - Area of the right triangle inscribed in the semicircle
By applying Pythagoras theorem in the given right triangle,
(Hypotenuse)² = (leg 1)² + (leg 2)²
= (21)² + (20)²
Hypotenuse = [tex]\sqrt{441+400}[/tex]
= [tex]\sqrt{841}[/tex]
= 29
Since, hypotenuse of the right triangle is the diameter of the circle.
Therefore, radius of the circle = [tex]\frac{29}{2}[/tex]
= 14.5 in.
Area of the circle = πr²
= π(14.5)²
= 660.519
≈ 660.52 in²
Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(21)(20)[/tex]
= 210 in²
Area of the shaded region = 660.52 - 210
= 450.52 square inch