Given:
Distance between parallel sides = 2 cm
Sum of parallel sides = 10 cm

To find: Area of the parallelogram

Solution:
We know that the area of a parallelogram is given by the formula:

Area = base × height

Here, the base of the parallelogram is the distance between the parallel sides, which is given as 2 cm.

Let's find the height of the parallelogram using the given information.

Let the lengths of the parallel sides be a and b, such that a > b. Then, we have:

a + b = 10 (given)
a - b = 2 (distance between parallel sides)

Adding the above two equations, we get:

2a = 12
a = 6 cm

Substituting the value of a in either of the above two equations, we get:

b = 4 cm

Now, the height of the parallelogram can be found using the formula:

height = (area of parallelogram) / (base)

We know that the base is 2 cm, and the area is yet to be found. Let the height be h.

So, we have:

h = (area of parallelogram) / 2

And also, we know that:

area of parallelogram = base × height

Substituting the value of height in terms of area, we get:

h = (area of parallelogram) / 2

=> area of parallelogram = 2h

=> area of parallelogram = 2 × base × height

Substituting the given values, we get:

area of parallelogram = 2 × 2 × h
area of parallelogram = 4h

We need to find the value of h. Let's use the Pythagorean theorem to find it.

In the right triangle formed by the height, base, and one of the sides of the parallelogram, we have:

(base/2)^2 + h^2 = (a/2)^2

Substituting the given values, we get:

(1)^2 + h^2 = (3)^2

h^2 = 8

h = √8

h = 2√2 cm

Now, substituting the values of base and height in the formula for area, we get:

Area = base × height
Area = 2 cm × 2√2 cm
Area = 4√2 cm²
Area ≈ 5.66 cm²

Therefore, the correct option is (b) 10 cm².