If your first thought of a trapezoid was either a flying circus act or a muscle in the shoulder, this blog is for you!

First, a minor let down. A trapezoid is nothing exotic as double summersault through the air. But it is pretty nifty. This is a trapezoid:

What’s a trapezoid, then? *It’s a shape with four sides. Of the four sides, two of them are parallel. *

In this case, the top and bottom lines are parallel. The side lines will eventually intersect if they continue downward.

A trapezoid’s side lengths don’t matter. Two sides can be the same, as shown above. Or they can all be different, like these:

The top and bottom lines are still parallel, even though no two lines have the same length.

***Burning Question: Is a rectangle a trapezoid? Nope. A trapezoid can only have ONE set of parallel lines. Rectangles (and squares) have two sets! (Now ask yourself if a square can be a rhombus. To find out, start a conversation with an online math tutor😊)

****Fun note: There is also a shape called a TRAPEZIUM, which is a four-sided shape with no parallel sides, like this:*

This is not a trapezoid.

Now that we have a trapezoid, what do we do with it? How can find its area?

Why do we need to find its area? It’s like the old saying goes:

*There was an old woman who lived in a shoe*

*She had so many sons, she didn’t know what to do.*

*So she sliced up the shoe, like a loaf, and gave them to her boys*

*“This is your home, enjoy the trapezoid!”*

So, how much living space did each kid have?

Let’s say this is the cross section of the shoe slice:

How to figure out the area?

An area for a trapezoid is the SUM of the *two parallel sides*, divided by 2, and then MULTIPLIED by the *height. *The *height* is a *perpendicular line* between the *two parallel sides.*

Here we go:

So let’s give some dimensions to the shoe:

Let’s plug in those values:

^{}

Don’t forget this is squared meters since we are considering two dimensions! We multiplied the labels to get meters^{2}

Fun addition: volume!

But the shoe slice also has three dimensions: **length**!

It is very easy to figure out the volume of a trapezoid! Simply* multiply* the area by its **length**!

Since we already know the area, let’s just say that the generous old woman gave each son a slice of shoe that was two meters long. Plug in the numbers again:

^{}

**Note that when measuring by volume, we are dealing with three dimensions, so the figure is cubed!*

*Hip hooray!*

A simple formula to measuring half angles.