Answer:
226.084 sq.m.
Step-by-step explanation:
Radius of circle = 18.6 cm
Area of sector = [tex]\frac{\theta}{360^{\circ} }\pi r^2[/tex]
Area of sector = [tex]\frac{123}{360} \times 3.14 \times (18.6)^2[/tex]
Area of sector = [tex]371.157 m^2[/tex]
Area of triangle = [tex]\frac{1}{2} \times a \times b \times Sin x[/tex]
a = OA = radius = 18.6 cm
b = OB = radius = 18.6 cm
x =123 °
Substitute the values in the formula
Area of triangle = [tex]\frac{1}{2} \times 18.6 \times 18.6 \times Sin 123[/tex]
Area of triangle = [tex]145.073 m^2[/tex]
So, Area of shaded region = Area of sector - Area of triangle
=[tex]371.157 m^2-145.073 m^2[/tex]
=[tex]226.084 m^2[/tex]
Hence the area of the shaded region is 226.084 sq.m.
