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. The other three faces are rectangles. To
find their areas, you need first to determine the height of the solid. If the area
of the base is 6, and the volume is 30, then
So the areas of the three rectangular faces are 3 × 5 = 15, 4 × 5 = 20, and 5 × 5 =
25 . The total surface area, then, is 6 + 6 + 15 + 20 + 25 = 72. The answer is (E).
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