Areas of Parallelograms

This sketch shows how the areas of two parallelograms with the same base and height will always have the same area. You can drag points

and

to change how the parallelograms look.

Given that

is a parallelogram and

is also a parallelogram and

In other words, the two parallelograms share base

and, since their opposite sides are on the same line, they also have the same height. We want to prove their areas are equal.

Explain why

Case I

Assuming

is to the left of

Explain why the two green trapezoids have the same area

Explain why .

Assuming

is to the right of

Explain why .