Geometry: LEARN Area Formulas

In geometry class in high school, I was always given the area formulas for 2d and 3d shapes. But I had no explanation for how these formulas came to be.  Understanding these formulas was never expected of me, but it was something that I expected to be taught. If you only came to this blog to look at the area formulas, I encourage you to read on and learn more math. Here is an image that showcases many different area formulas.

Area Formulas, Volume Formulas, 2d, 3d, radius, height, length, width

Let’s understand these formulas now.

How do we bring shapes from a simple form into a more complicated form: a 1d line to a 2d shape, or a 2d shape to a 3d solid? We multiply. By something. It’s as simle as that in ALL cases. The simplest case is a square.

Shapes, Cube, Square, Area Formulas, Volume Formulas

We start with a line, and if we want to extend the line into a new dimension, we multiply by how much we want to extend it by, creating a rectangle (in this case a square). Then to turn a square into a cube, we multiply by how much we want to extend the square by. Notice that this is the same explanation for if you wanted to make a rectangle and a recangular prism.

You ponder, “Surely, it can’t be that simple!”

“Oh, but it can! And don’t call me Sherley.”

“Fine. Maybe for a square this works (that’s the easy one) but… what about circles?”

 

2560x1440-white-solid-color-background

We start with a line, and if we want to extend the line into a new CIRCULAR  dimension, we multiply by how much we want to extend it by. Circles, however use a special multiplier (you might have heard of pi). So to create a circle from a line (assuming the line is our radius), we multiply the length of the line times itself times π. To turn a circle into a cylinder, we multiply by how tall we want to extend the circle by just like we did with a square to a cube or a rectangle to a rectangular prism.

To make a circle a sphere… we multiply the area of or circle by (4/3) times the radius. But why 4/3? And what even is pi?!?! Find out next time!

 

 

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