Area of Parallelogram/Rectangle

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

Proof
Let $ABCD$ be a rectangle.


 * [[File:Cua1.PNG]]

Then construct the square with side length $\left({AB + BI}\right)$ where $BI = BC$, as shown in the figure above.

Note that $\square CDEF$ and $\square BCHI$ are squares.

Thus $\square ABCD \cong \square CHGF$.

Since congruent shapes have the same area, $\left({ABCD}\right) = \left({CHGF}\right)$ (where $\left({FXYZ}\right)$ is the area of the plane figure $FXYZ$).

Let $AB = a$ and $BI = b$.

Then the area of the square $AIGE$ is equal to: