Answer:
38.1 cm²
Step-by-step explanation:
Area of the sector = centre angle / 360⁰ × πr² (take π = 3.14)
Area of the sector = 150⁰/360⁰ × 3.14 × 6²
Area of the sector = 150⁰/360⁰ × 3.14× 36
Area of the sector = 47.1 cm²
Area of the triangle = 1/2 × ab × sin (centre angle), where a = b = 6cm.
Area of the triangle = 1/2 × 6 × 6 × sin 150⁰
Area of the triangle = 6 × 3 × sin 30⁰
Area of the triangle = 6 × 3 × 1/2
Area of the triangle = 3 × 3
Area of the triangle = 9 cm²
Therefore,
Area of the shaded region = Area of the sector - Area of the triangle
Area of the shaded region = (47.1 - 9) cm²
Area of the shaded region = 38.1 cm²
