calculating area of a trapezoid
Posted By StudyGate
Trapezoid Training

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:

trapezoid training online

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:

area of a trapezoid online learning

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:

trapezium area formula

So let’s give some dimensions to the shoe:

calculating area of a trapezoid

Let’s plug in those values:

finding trapezoid area

Don’t forget this is squared meters since we are considering two dimensions! We multiplied the labels to get meters2

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!

trapezoid volume formula

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:

calculating trapezoid volume

*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.