Question

Explain why a parallelogram can have two different heights and two different bases but the product bh is the same in either case.

a) The area of a parallelogram depends only on the sum of the lengths of the two bases.
b) The area of a parallelogram is invariant under transformations.
c) The height of a parallelogram is perpendicular to both bases, maintaining a constant area.
d) The product bh is not constant; it depends on the specific parallelogram.

Answer 1

A parallelogram's area remains constant regardless of which base and corresponding perpendicular height are used, as altering one dimension compensates the other to maintain the product bh equal.

Step-by-step explanation:

A parallelogram can have two different heights and two different bases, but the product of base and height (bh) stays the same for both cases because the area of a parallelogram is the product of the base and the corresponding perpendicular height. Choosing different bases for the calculation only alters the corresponding height. For example, if you increase the base length by choosing the longer side of the parallelogram, the corresponding perpendicular height decreases in such a way that the product of the new base and the new height remains equal to the area calculated with the original base and height. This happens because the area of a parallelogram is consistent, no matter which base and corresponding height are used.