Answer:
C.47.2 square in
Step-by-step explanation:
We are given that
Radius,r=7 in
Central angle,[tex]\theta=\frac{4\pi}{5}[/tex]rad
We have to find the area of segment of circle O.
Area of segment=Area of sector-Area of triangle
Area of triangle=[tex]=\frac{1}{2}\times base\times height=\frac{1}{2}\times 7^2sin(\frac{4\pi}{5})=14.4in^2[/tex]
Area of sector=[tex]\frac{\theta}{2\pi}\times \pi r^2=\frac{4\pi}{10\pi}\times \pi (7)^2=61.57 in^2[/tex]
Area of segment=(61.57-14.4)square in
Area of segment=47.17 square in[tex]\approx 47.2in^2[/tex]
Hence, option C is true.
