The formula for the area of a circle is pir^2. The radius of this circle is 3 feet. The area of the circle is 3^2pi, which is equal to 9pi ft^2. Since the angle of the arc that is shaded is 50 degrees, it is 50/360 of the whole circle. The area of that specific segment plus the area of the isosceles triangle is the area of a sector of the circle. The latter would be the total area of the circle multiplied by the portion of the circle that segment takes up.
The area is then 9pi * 50/360, which is 5/4pi ft^2~~ 3.93 " ft"^2 .
To find the area of the isosceles triangle, note that its base is 2 times 3" ft" times sin(50^circ)/2, while the height is 3" ft" times cos (50^circ)/2. Thus, the area is
1/2 times "base" times "height" = 1/2 times 2 times 3" ft" times sin(50^circ)/2 times 3" ft" times cos (50^circ)/2 = 4.5" ft"^2times sin50^circ ~~ 3.45" ft"^2
Thus, the area of the shaded part is
3.93 " ft"^2- 3.45" ft"^2 = 0.48" ft"^2 ~~ 0.5" ft"^2(to the nearest tenth)
