# Measurement (second half)

In our seventh lesson of measurement we learned how to find the surface area and volume of a rectangular based pyramid. It takes a while and you have to make sure that your formulas are correct to get the right answer. A trick is to write out everything you do. For example you can directly draw the shape of the face it is that you are trying to calculate the area of. This helps to keep track of everything you do and makes it easier to visually see.

Surface Area:

First you have to find the two slant heights of the pyramid. A rectangular based pyramid has two slant heights because the base side lengths are not the same. You find the slant heights by using pythagorean theorem on each triangular face.
Once you find the two slant heights, you find the area of each triangular face. Then you add those to the base area. (Make sure to put the coefficient 2 in front of each triangular face’s area. You do this because it tells you that two of the four triangular faces have the same area.)
You add the each face by writing out how to get the area of each triangular face and then the area of the base. You write them all out side by side and simplify where you can. Lastly you multiply the numbers left after you have simplified.
The number that is left is the surface area of the rectangular prism.
I know this sounds hard, so an example will make it easier to see.

Volume:

To get the volume of a rectangular based pyramid you multiply 1/3 by the area of the base by the height of the pyramid.
You should already have the area of the base from finding the surface area, so we just use that to easily find the volume. (You should be able to do the whole equation on your calculator.)
Here is an example using the same dimensions that I used for finding the surface area above.