A trapezoid is a quadrilateral with exactly 1 pair of parallel sides.
![](https://static.mathigon.org/cms/6380a71753c4320fbd6519740595f0fe.png)
In the Polypad canvas below, create different trapezoids to explore area of trapezoids. Here is an example to get you started:
Are you able to use your examples to create a formula for the area of any trapezoid?
Solution
You may have noticed the area seems to be equal to the height multiplied by half of the sum of parallel sides a and b. Indeed, the general approach for the area of any trapezoid is
.
Try and use some of the visuals below to write up a proof for this formula:
![](https://static.mathigon.org/cms/e81500dc614b3b21989353d2ed3abcd1.gif)
![](https://static.mathigon.org/cms/c0fe46cbe29cde3eb098cc386b1704b4.gif)
![](https://static.mathigon.org/cms/132ec97b9b86fb5472c29cb13dccd7d3.gif)