216 Part 3: The Shape of the World
Most of the examples you see around you are what mathematicians call right prisms. That means
that the two bases are positioned in line with one another so the sides meet the bases at a right
angle. It is possible to make a prism that isn’t right and seems to lean to one side, but you don’t
see them being used very often.DEFINITION
A prism is a right prism if the parallelograms meet the bases at right angles.Surface Area
Questions about the surface area can be answered by finding the area of each face of the solid
and adding them up. It’s often easier just to disassemble the prism, and then think about the
area of the pieces. Do you have a triangular prism? That’s two triangles for the bases and three
rectangles around the sides. Check for the dimensions of each and go to work on the areas.MATH TRAP
Don’t automatically assume that all the parallelograms are the same size. If your bases
are regular polygons, it might be true, but make sure you check first.Suppose you’re looking for the surface area of a triangular prism that stands 6 inches high, and
the triangular bases are equilateral triangles with sides 3 inches long. You need to find the area of
the two equilateral triangles and the area of the 3 rectangles.Each rectangle is 6 inches long and 2 inches wide, so each has an area of 12 square inches.
The equilateral triangles have a base of 2 inches, but you need a height, and for that you have
to remember your 30-60-90 right triangles. The height of an equilateral triangle is half the
length of a side times the square root of three, or in this case, 13. The area of each triangle is
1
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