To find the area of a sector, we need to know the radius and the angle of the sector. However, in this question, we are given the perimeter of the sector and the radius.

Let's start by understanding the perimeter of a sector. The perimeter of a sector is the sum of the lengths of the arc and the two radii that form the sector. In this case, we are given that the perimeter is 16.4 cm.

Let's assume the angle of the sector is θ. Since the length of the arc is proportional to the angle, we can write:

Length of arc = (θ/360) * 2πr

where r is the radius of the circle.

In this question, the length of the arc is equal to the perimeter minus the sum of the two radii:

Length of arc = 16.4 cm - 2 * 5.2 cm

Simplifying, we have:

Length of arc = 16.4 cm - 10.4 cm
Length of arc = 6 cm

Now, we can use the formula for the area of a sector:

Area of sector = (θ/360) * πr^2

Substituting the given values, we have:

Area of sector = (θ/360) * π * (5.2 cm)^2

We need to find the value of θ. To do that, we can use the fact that the length of the arc is proportional to the angle:

Length of arc = (θ/360) * 2πr

Substituting the given values, we have:

6 cm = (θ/360) * 2π * 5.2 cm

Simplifying, we have:

6 cm = (θ/360) * 10.4π cm

Dividing both sides by 10.4π cm, we get:

(θ/360) = 6 cm / (10.4π cm)

(θ/360) = 0.182

Multiplying both sides by 360, we get:

θ = 0.182 * 360

θ = 65.52 degrees

Now, substituting the value of θ into the formula for the area of the sector, we have:

Area of sector = (65.52/360) * π * (5.2 cm)^2

Calculating further, we get:

Area of sector = (65.52/360) * 3.14 * (5.2 cm)^2

Area of sector ≈ 15.6 cm^2

Therefore, the correct answer is option B) 15.6 cm^2.