Given,
Radius = 5.7 cm = OA = OB [from the figure shown above]
Perimeter of the sector = 27.2 m
Let the angle subtended at the centre be θ
We know that,
Length of arc = θ/360 ∗ 2πr m
Now, Perimeter of the sector = θ/360 ∗ 2πr + OA + OB
27.2 = θ/360 ∗ 2π x 5.7 cm + 5.7 + 5.7
27.2 – 11.4 = θ/360 ∗ 2π x 5.7
15.8 = θ/360 ∗ 2π x 5.7
θ = 158.8°
So, the area of the sector = θ/360 ∗ πr2
Area of the sector = 158.8/360 ∗ π 5.72
Solving the above, we get
Area of the sector = 45.03 m2
