Area of Parallelogram/Parallelogram

Theorem
The area of a parallelogram equals the product of one of its bases and the associated altitude.

Proof

 * Area-of-Parallelogram.png

Let $ABCD$ be the parallelogram whose area is being sought.

Let $F$ be the foot of the altitude from $C$

Also construct the point $E$ such that $DE$ is the altitude from $D$ (see figure above).

Extend $AB$ to $F$.

Then:

Thus:
 * $\triangle AED \cong \triangle BFC \implies \paren {AED} = \paren {BFC}$

So:
 * $\paren {ABCD} = EF \cdot FC = AB \cdot CF$