Question

What is the area of a sector with a central angle of 210 degrees and a diameter of 4.6 m? Round the answer to the nearest tenth.

Answer 1

We know that the area of a sector is given by:
A = 1/2r²∅; where ∅ is in radians
210/360 = ∅/2π
∅ = 7π/6
r = 4.6/2 = 2.3 m
A = 0.5 x 2.3² x 7π/6
A = 3.08 m²

Answer 2

The area of the sector is the area of the circle * [210 /360]

This is obtained by considering that the area of the sector is proportional to the ratio of the sector angle to the entire circle angle.

Also you can say area of the sector / are of the circle = angle of the sector / 360°

Then, area of the sector = π(2.3m)^2 *300 / 360 = 13.9 m^2