Notice that It's All the Same Formula when finding the area of a triangle or quadrilateral.

$$(the \ average \ of \ the \ top \ and \ bottom) \times height$$

Squares, Rectangles, Parallelograms, and Rhombuses

In the case of these polygons, the top and the bottom are the same, so the average is simply the bottom (or the top). And the formula is:

$$base \times height$$

Trapezoids

Of course trapezoids have the average of the top and bottom embedded into the formula itself:

$$(average \ of \ the \ bases) \times height = \frac{base_1 + base_2}{2} \times height$$

But It Even Works for Triangles!

Notice how the bottom is $b$ and the top has a "length" of $0$. So, if we find the average of the bottom and top ($b$ and $0$) and then multiply it by the height, do we get the more familiar triangle area formula? Let's see.

$$\frac{b+0}{2} \times h = \frac{b}{2} \times h = \frac{bh}{2}$$

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