Math Help [Request Topics]

Areas, Volumes, and Fractions

Any photos that are not hand written equations or drawings are not owned by me. They belong to their respective creators. I only created the photos using blue marker on whiteboard.

So, when it comes to finding areas and volumes of shapes, at a basic level, it will take a lot of memorization of formulas. Unfortunately, the reason behind why a lot of the equations exist requires a higher level of mathematics and an understanding of proofs (you don't have to worry about these right now). There are basic shapes that have simple formulas for finding the area, and these play a role in finding the areas and volumes of more complicated shapes. For now, we'll stick with the basics. Since I can't explain the derivation of these formulas without overcomplicating things, I'll draw out a table with the equations, shape, and diagram to go along with it. To help with understanding the notation:

A: Area

w: width

l: length

s: side

r: radius

h: height

a: arbitrary side length

b: another arbitrary side length

π: pi (3.1415926535897932384626433832795028841971693993...) (or for short: 3.14 or 3.14159)

These are most (if not all) of the formulas you would have to memorize. But I believe that you can do it! The last two formulas (circle and ellipse) you may or may not see, depending on grade level, but are helpful to memorize nonetheless. We can use these basic area formulas to find the area of much more intricate shapes. I'll show an example of this, below.

As we can see here, this 2D ice-cream cone can be split into two separate shapes: a semi-circle and a triangle. For those who don't know what a semi-circle is, a semi-circle is just half of a full circle. As such, the area of a semi-circle is just half the area of a full circle. To get the full area of the ice-cream cone, all we do is add the two areas together. 

In most of these types of problems, more complicated shapes can be broken down into more basic shapes that we know the area of and then we can add all these areas together to get the full area of the shape. I have a practice problem below for you to try below.