If the remaining faces are rectangles (as in the figure 2nd 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 5-sided base is a pentagonal prism, a prism with a 6-sided base is a hexagonal prism, etc.
The volume V of a right prism is given by the formula
V = Bh,
where B is the area of the base and h is the height.
Find the volume of the prism shown.
The height of the prism is 10 cm. The base is a right triangle with legs of length 5 cm and 12 cm, so
Therefore, the volume is
Note that for a rectangular prism, the volume formula becomes simply
V = lwh,
where l is the length of the base, w is the width of the base, and h is the height of the prism.
The surface area S of a prism is given by the formula
S = 2B + Ph,
where B is the area of the base of the prism, P is the perimeter of the base, and h is the height.
So the perimeter of the base is 5 + 12 + 13 = 30 cm. We already know the base area is 30 cm2. So,
You many 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 L = Ph.