Alice is making an octahedron out of origami. The last step requires her to blow into the octahedron to fill it up. A square pyramid on top of an upside down square pyramid the same size. The length of each side of the square base is a and the height of each pyramid is b. Which expression represents the volume of air she will need to inflate the octahedron?

Total volume is volumes of both square pyramids.

Volume of a tetrahedron is 1/3 times corresponding prism, and a square pyramid has two tetrahedrons.

Thus, volume of on square pyramid:

Since there are two of them, total volume is:

$\boxed{\frac{2a^2b}{3}}$

6(h+1)/2=a

a=area

step-by-step explanation:

its the same thing as a square or rectangle but after multiplying two sides you need to divide it by two.