The surface area is the sum of the areas of the faces. To find the areas of the faces, you need to
figure out what kinds of polygons they are so that you’ll know what formulas to use. Start with the
bases, which are said to be “triangles with sides of lengths 5, 12, and 13.” If these side lengths don’t
ring a bell in your head, go back and study your Pythogorean triplets. This is a 5-12-13 triangle,
which means it’s a right triangle, which means that you can use the legs as the base and height to
find the area:
That’s the area of each of the bases. Now call the height of the solid h. The other three faces are
rectangles with areas 5 × h, 12 × h, and 13 × h. The total surface area, then, is 30 + 30 + 5h + 12h + 13h
= 60 + 30h.
Since the problem tells us that the surface area is 360,
Volume = base × height = 30 × 10 = 300. The answer is (C).
PICTURING SOLIDS
You might have thought that solid geometry questions are difficult because of the formulas. As you
have seen, however, using formulas is by definition routine. It’s the nonroutine problems that can
be the most challenging. Those are the solid geometry problems that require you to visualize, like
Example 4.
Example 4