For this activity, we will demonstrate how the area formulae in this lesson form an axiomatic system. We just need to decide which area formula should be the axiom... Duration: 5:35

Now that we have selected the square as our axiom, let's prove that the area formula for a rectangle based on that assumption. Duration: 14:47

The word rectify means to correct or make something right, and it's derived from the same Latin word as rectangle. In geometry, rectify means to transform a shape into a rectangle. That is exactly how we will prove the area formula for a parallelogram. Whereas a less technologically-minded instructor might use a bit of construction paper, crayons, and some safety scissors for this demonstration, we will use an app called Geogebra. Duration: 14:16

Using Geogebra once again, we demonstrate how to derive the area formula of a triangle from a parallelogram. Duration: 10:08

Next up is a trapezoid. Looks like we can do this using the same method as the parallelogram, but as clichés will have you know, looks can be deceiving. Speaking of, the video below looks identical to the video above, but it's totally not. Duration: 4:13

It's time to go raid your kitchen. We are looking for a flour tortilla and a pair of kitchen scissors, though I believe a corn tortilla will do in a pinch. As you will see, these are ingredients necessary to derive the area formula for a circle. Might as well grab yourself a healthy snack while your in the kitchen, and maybe a glass of water. It's important to stay hydrated. Duration: 4:35

In the previous video, we were able to use a pair of kitchen scissor to turn a common tortilla into a parallelogram. Now let's do the math to actually derive the formula for the area of a circle. If you are interested, here is the desmos demonstration used in the video. Duration: 6:14