Question

Find the area of the shaded region. Round the the nearest tenth.

Answer 1

Answer:

226.084 sq.m.

Step-by-step explanation:

Radius of circle = 18.6 cm

Area of sector = $\frac{\theta}{360^{\circ} }\pi r^2$

Area of sector = $\frac{123}{360} \times 3.14 \times (18.6)^2$

Area of sector = $371.157 m^2$

Area of triangle = $\frac{1}{2} \times a \times b \times Sin x$

a = OA = radius = 18.6 cm

b = OB = radius = 18.6 cm

x =123 °

Substitute the values in the formula

Area of triangle = $\frac{1}{2} \times 18.6 \times 18.6 \times Sin 123$

Area of triangle = $145.073 m^2$

So, Area of shaded region = Area of sector - Area of triangle

                                            =$371.157 m^2-145.073 m^2$

                                            =$226.084 m^2$

Hence the area of the shaded region is 226.084 sq.m.