Express the area of the shaded region in the accompanying fi

Express the area of the shaded region in the accompanying figure in terms of r and theta. (Assume that theta is in radians.)

Solution

Solution:

Shaded portion is segment of the circle

where r is radius and angle by radians

area of shaded portion = area of sector - area of unshaded region

= r²/2 - sin() r²/2

= ( - sin() ) r²/2

Answer: Area of shaded portion :  ( - sin() ) r²/2