To find the area of a sector, you can use the following formula:
Area = (θ/360) x πr^2,
where θ is the central angle and r is the radius of the sector.
In this case, the diameter is given as 4.6 m, so we can find the radius by dividing the diameter by 2:
radius = diameter/2 = 4.6/2 = 2.3 m.
The central angle is given as 210°. The formula requires the angle to be in radians, so we need to convert it by multiplying by π/180:
θ = 210° x (π/180) ≈ 3.66519143 radians.
Now, we can substitute the values into the formula to find the area:
Area = (θ/360) x πr^2 = (3.66519143/360) x π(2.3)^2 ≈ 0.0337 x π x 5.29 ≈ 0.5305 m^2.
Rounding to the nearest tenth, the area of the sector is approximately 0.5 m^2.