The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. What is the area of the sector ? 

Given:

The perimeter of a sector of a circle of radius = 16.4 cm

The radius of a sector of a circle of radius 5.2 cm.

Formula used:

The perimeter (P) of a sector of a circle with radius (r) and central angle (θ) is 

P = θr + 2r

Area of sector = (θ/2π) πr²

Calculation:

Using the given values, we have:

16.4 = θ(5.2) + 2(5.2)

16.4 = 5.2θ + 10.4

θ = 6/5.2 ≈ 1.153 radians (rounded to three decimal places)

Area of sector = (θ/2π) πr2

A = (θ/2π)πr²

A = (1.153/2π) × π(5.2)²

A = (1.153 × 5.2 × 5.2)/2 

A = 15.6 cm² (rounded to one decimal place)

Therefore, the area of the sector is approximately 15.6 cm².