If the remaining faces are rectangles (as in the figure nd figure above), then the prism is called a right prism . School level math books usually only talk about right prisms, and sometimes when they say prism they mean right prism.
A triangular prism is a prism with a triangular base, like the figure on the right. A rectangular prism is a prism with a rectangular base. (The cube is a special case.) Similarly, a prism with a -sided base is a pentagonal prism , a prism with a -sided base is a hexagonal prism , etc.
Volume of a Prism
The volume of a right prism is given by the formula
where is the area of the base and is the height.
Find the volume of the prism shown.
The height of the prism is cm. The base is a right triangle with legs of length cm and cm, so
Therefore, the volume is
Note that for a rectangular prism, the volume formula becomes simply
where is the length of the base, is the width of the base, and is the height of the prism.
Surface Area of a Prism
The surface area of a prism is given by the formula
where is the area of the base of the prism, is the perimeter of the base, and is the height.
So the perimeter of the base is cm. We already know the base area is cm 2 . So,
You may sometimes be called upon to find the lateral surface area of a prism. This just means the surface area of the faces not including the bases, or .