Volume of rectangular pyramids using cubes | Grade 7 (TX TEKS) | Khan Academy

We'll be exploring the volumes of rectangular pyramids today with cubes and rectangular prisms. This is a cube; all the sides are the same length. To find the volume of a cube, I can multiply the length by the width by the height. For example, if the length of the cube is five and all sides are the same, then to find the volume I would do 5 * 5 * 5 = 125 cm cubed.

I can break this prism into three rectangular pyramids that are all congruent. So now we have a cube that's actually made out of three rectangular pyramids, and we can see here that all of the rectangular pyramids are congruent. The base of each rectangular pyramid is a square. The square is the same size as one face of our cube, and they all have the same height.

Since all of these rectangular pyramids are congruent, they all have the same volume. To summarize so far, three congruent pyramids can form a cube, and the volume of one of the pyramids will be 1/3 the volume of the entire cube. This is true for all cubes, but what about other rectangular prisms where the sides have different lengths?