Answer:
Area of the shaded region = 1.92 cm²
Step-by-step explanation:
From the picture attached,
Area of the shaded region = Area of the sector OMN - Area of the triangle OMN
Area of sector OMN = [tex]\frac{\theta}{360}(\pi r^{2})[/tex]
Here, θ = Central angle of the sector
r = radius of the sector
Area of sector OMN = [tex]\frac{50}{360}(\pi )(6)^2[/tex]
= 15.708 square cm
Area of ΔOMN = 2(ΔOPN)
Area of ΔOPN = [tex]\frac{1}{2}(OP)(PN)[/tex]
Area of ΔOMN = OP × PN
In ΔOPN,
sin(25°) = [tex]\frac{PN}{ON}[/tex]
PN = ONsin(25°)
= 6sin(25°)
= 2.536 cm²
cos(25°) = [tex]\frac{OP}{ON}[/tex]
OP = ONcos(25°)
OP = 6cos(25°)
OP = 5.438 cm
Area of ΔOMN = 2.536 × 5.438
= 13.791 cm²
Area of the shaded region = 15.708 - 13.791 = 1.917 cm²
≈ 1.92 cm²
