Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 16: Surface Area and Volume 217

The total surface area is the two triangles plus the three rectangles or 23 312 =
36 2 3 39.46 square inches. The area of the three rectangles is called the lateral area.

DEFINITION

The lateral area of a prism is the total of the areas of the parallelograms surrounding

the bases.

Coming up with a formula for that process is difficult because of all the different possibilities for
the number of edges of the base and therefore the number of rectangles around it. Add the fact
that the bases may or may not be regular polygons, and it’s amazing that you can get any kind of
formula, but you can.

Imagine a prism 6 inches high whose bases are 3-4-5 right triangles. The surface area is

2
1
2
34 36 4 6 56. Let’s rewrite those last three pieces, so the surface area looks like

this: 2 1
2

34 63 4 5. The sum in the parentheses, 3 + 4 + 5, is the perimeter of the base.

So you can say the surface area of the prism is two times the area of the base plus the height (h)
times the perimeter of the base. If you use B for the area of the base and P for the perimeter of
the base, the formula is SA = 2B + hP.

The surface area of a rectangular solid, is SA = 2LW + 2Lh + 2Wh = 2LW + h(2L + 2W) = 2(area
of base) + h(perimeter of base). Let’s apply this to the rectangular prism shown.

SA = 2(14 v 8) + 30(2 v 14 + 2 v 8)

= 2(112) + 30(28 + 16)

= 2(112) + 30(44)

= 224 + 1320

= 1544

The surface area is 1,544 square centimeters.

30 cm

14 cm

8 cm