The area of a rectangle can be found when we know the lengths of its sides. Is the same true for a parallelogram? That is, can we find the area of a parallelogram when we know the lengths of its sides? 
Why or why not?                                                                                                                                                                           [Page No. 131]

No, the area of a parallelogram cannot be determined from the lengths of its sides alone. For a rectangle, knowing the lengths of the two sides is enough because the angle between them is always $90^{\circ}$. The area is therefore fixed, i.e., $\text{length} \times \text{width}$.
However, a parallelogram with the same side lengths can have different shapes. By changing how much the figure is slanted, we change the perpendicular distance (height) between the parallel sides while keeping all four side lengths unchanged.

As the parallelogram becomes more slanted, its height decreases, so its area decreases. When it is less slanted, the height increases, so the area increases. Thus, several parallelograms can have the same side lengths but different areas.

Therefore, the side lengths alone are not sufficient to find the area of a parallelogram. We must also know its height (or equivalently, the angle between the sides).

Since, area of a parallelogram = base $\times$ height, the area depends on both the base and the height, not just on the lengths of the sides.