To find the area of the parallelogram, we need to find the length of one of its sides and the height of the parallelogram.

Finding the length of a side:
We have the equations of four sides of the parallelogram:
1) x + 2y + 3 = 0
2) 3x - 4y + 5 = 0
3) 2x + 4y + 5 = 0
4) 3x - 4y - 10 = 0

We can find the intersection points of these lines to get the vertices of the parallelogram. Let's solve equations (1) and (2) to find the intersection point of sides 1 and 2.

1) x + 2y + 3 = 0
2) 3x - 4y + 5 = 0

By solving these equations, we get x = -1 and y = -2. So the intersection point of sides 1 and 2 is (-1, -2).

Similarly, we can find the intersection points of the other pairs of sides: (2, 0) for sides 2 and 3, and (1, 1) for sides 3 and 4.

Now, we can find the length of one of the sides by calculating the distance between two adjacent vertices. Let's find the length of side 1.

Using the distance formula, the length of side 1 is:
√[(-1 - 2)^2 + (-2 - 0)^2]
= √[(-3)^2 + (-2)^2]
= √[9 + 4]
= √13

Finding the height of the parallelogram:
The height of the parallelogram is the perpendicular distance between one of the sides and the opposite side. Let's find the height by calculating the distance between side 1 and side 3.

Using the distance formula, the height of the parallelogram is:
√[(-2 - 0)^2 + (0 - 0)^2]
= √[(-2)^2 + 0]
= √4
= 2

Calculating the area of the parallelogram:
The area of a parallelogram is given by the formula: Area = base × height.

In this case, the base is the length of side 1, which is √13, and the height is 2.

Therefore, the area of the parallelogram is:
Area = √13 × 2
= 2√13

Simplifying the expression, we get:
Area = 2√13
= (2/√13) × (√13/√13)
= (2√13) / 13

So, the area of the parallelogram is 2√13/13.

Comparing the options:
a) 5/3
b) 5/4
c) 6/5
d) 8/11

We can see that none of the given options match the calculated value of the area, which is 2√13/13. Therefore, none of the options is correct.