Can two parallelograms with different shapes have the same area?

Sure. The area of a parallelogram is (length of base) times (vertical height).

Many pairs of numbers can have the same product, but if the (base / height)

of two parallelograms are different pairs of numbers, then their shapes are

different.

Example:

A rectangle is a parallelogram that's easy to work with.

Take two rectangles:

Rectangle #1: Length=6, Width=5, Area=30

Rectangle #2: Length=15, Width=2, Area=30

These rectangles certainly have different shapes. In #1, the length is 83% of

the width, and in #2, the length is only 13% of the width.

But they both have the same area.