Prisms

​A prism, this is a shape you might not encounter often, unless you buy a chocolate at an airport, or take apart binoculars. This is what it looks like, like a stick with a cross section in a shape of a polygon. It can actually be any polygon but here it's a triangle and therefore it's a triangular prism. A prism always has equal polygons at both ends so the prism sides are parallel. It is easy to calculate the volume of a prism, at least if have already learnt how to calculate the volume of a rectangular prism.

It's the area of the base times the height. ​ ​The distinction from the rectangular prism is that here, you can't just take any surface and call it the base. You have to take the polygon as a base or you'll get a wrong answer. Here the base so it's the area of the triangle is a triangle, we have to calculate. Be careful with the names here, because normally when we calculate the area of a triangle this is the segment we call the height. But in a prism, this is the height, so we have to call the triangle's height something else.

Let's call it a. The triangle's area is b x a / 2. This is the base. We then multiply the area of the base by the height of the prism, h, and get the volume. A triangular prism therefore has the volume, a x b / 2 x h.

A prism with a different base still has the volume equal to the area of the base times the height, even if you have to calculate the area of the base in a different way. ​ ​The surface area of a prism is easy to calculate. Look carefully at the prism and you'll see that it consists of two triangles and three rectangles. If you have the lengths of the prism's edges, you simply calculate the areas of the triangles and rectangles separately and add them together. You don't need any formula at all.