Question

why is the area of a rectangle base x height?
Why is a non-rectangular parallelogram base x height and is this true?

Answer 1

yes this is true. You can show it many ways. But basically if you consider the parallelogram made up of two vectors in a plane. The area is the cross product of these vectors. If you put b so that it is in the direction of one of the axis you have h as the component of the second vector in the opposite plane. So the cross product would give you base*height.

Answer 2

Area is measured in a fancy derived unit: "squared (unit)". I think it would be easiest to show if you split the rectangle into "unit squares;" i.e., they are squares of a side length of one unit.

A fast way to count the number of squares here inside the rectangle is simply multiplying your number of columns by your number of rows. Thus, base times the height.

A parallelogram is quite interesting as well. If we have a parallelogram here, consider rearranging things.

We only move pieces around, so the area has not changed. However, we effectively can fill the gap on one side of the parallelogram with the other side! Thus, it makes a rectangle. We already know the routine from there: base x height. :)