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

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 =

                     =

                     = 29

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

Therefore, radius of the circle =

                                                  = 14.5 in.

Area of the circle = πr²

                             = π(14.5)²

                             = 660.519

                             ≈ 660.52 in²

Area of the right triangle =

                                         =

                                         = 210 in²

Area of the shaded region = 660.52 - 210

                                            = 450.52 square inch

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