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Area inside the semi-circle and outside the triangle is  (91.125π - 120) in²

Solution:

Base of the triangle = 10 in

Height of the triangle = 24 in

Area of the triangle =

Area of the triangle = 120 in²

Using Pythagoras theorem,

Taking square root on both sides, we get

Hypotenuse = 23 inch = diameter

Radius = 23 ÷ 2 = 11.5 in

Area of the semi-circle =

Area of the semi-circle = 91.125π in²

Area of the shaded portion = (91.125π - 120)  in²

Area inside the semi-circle and outside the triangle is  (91.125π - 120)  in².