Answer:
The solution is 192.83 ft²
Step-by-step explanation:
We need to find out the shaded region of the provided figure
Area of sector calculated as [tex]S=\frac{\theta}{360} \pi r^{2}[/tex] and
Area of triangle is calculated as [tex]A=\frac{1}{2} r^{2} \sin \theta[/tex]
Area of circle is calculated as [tex]C=\pi r^{2}[/tex]
Where r is radius
so,
Area of sector is [tex]S=\frac{\theta}{360} \pi r^{2}[/tex]
[tex]S=\frac{100}{360} 3.14 (8.35)^{2}[/tex]
[tex]S=\frac{5}{18} 3.14 (8.35)^{2}[/tex]
[tex]S=\frac{5}{18} 218.92[/tex]
[tex]S=60.81[/tex]
Area of triangle is [tex]A=\frac{1}{2} r^{2} \sin \theta[/tex]
[tex]A=\frac{1}{2} (8.35)^{2} \sin 100[/tex]
[tex]A=\frac{1}{2}68.32[/tex]
[tex]A=34.16[/tex]
Area of circle is [tex]C=\pi r^{2}[/tex]
[tex]C=3.14 (8.35)^{2}[/tex]
[tex]C=3.14 \times 69.72[/tex]
[tex]C=218.92[/tex]
Area of segment = area of sector - area of triangle
= 60.81 - 34.16
= 26.09 ft²
Area of shaded region = area of circle - Area of segment
= 218.92 - 26.09
= 192.83 ft²
Therefore, the solution is 192.83 ft²
