Answer: Area of the Shaded region is 818.44 square in
Explanation:
The given circle has a radius of 27.8 in
Step 1: Calculate the area of complete circle
The area of a circle is given as
A=
A= 2427.948 square in
Step 2: Calculate the area of a small segment of circle making 150 degrees.
The complete circle is of 360 degree
So, Area of a small segment of circle making 150 degrees will be,
A'=(150/360) (2427.948 ) \pi
A'=1011.645 square in
Step 3: Calculate the area of the Shaded region
The small segment of the circle is made of a triangle in the blue and Shaded region part
Therefore,
A'= 1011.645 = Area of triangle + Area of Shaded region
Area of Shaded region= 1011.645 - Area of a triangle
For the area of a triangle, two sides are equal and the radius of the circle
Therefore, It is an isosceles triangle
Area of triangle is given by = (1/2)(base)(height)
height = 27.8 cos (75)= 7.195169
base = 2x 27.8sin(75)=53.705
Area of triangle is given by = (1/2)(53.705)(7.195169)=193.205
Area of Shaded region= 1011.645 - Area of a triangle
Area of Shaded region= 1011.645 - 193.205 =818.44 square in
Thus, the Area of the Shaded region is 818.44 square in