Question

Find the area of the shaded region. Round to the nearest hundredth

Answer 1

Area of the shaded region = 450.52 square inch

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 =
`√(441+400)`

=
`√(841)`

= 29

Since, hypotenuse of the right triangle is the diameter of the circle.

Therefore, radius of the circle =
`(29)/(2)`

= 14.5 in.

Area of the circle = πr²

= π(14.5)²

= 660.519

≈ 660.52 in²

Area of the right triangle =
`(1)/(2)(\text{Base})(\text{Height})`

=
`(1)/(2)(21)(20)`

= 210 in²

Area of the shaded region = 660.52 - 210

= 450.52 square inch