Find the area of the segment shaded in blue in the figure of

Find the area of the segment (shaded in blue in the figure) of a circle whose radius is 3 feet, formed by a central angle of 55°. [Hint: Subtract the area of the triangle from the area of the sector to obtain the area of the segment.]

Solution

Area of traingle = (1/2)a*bsinA = (1/2)(3)(3)sin55

= 3.686 sq-ft

Area of sector = (55/360)*pi*(3)^2 = 4.319 sq-ft

Area segment in blue = Area of sector - area of triangle = 4.319 - 3.686

=0.634 sq-ft