Idiot\'s Guides Basic Math and Pre-Algebra

218 Part 3: The Shape of the World

CHECK POINT

Find the surface area of each prism. SA = 2B + hP

1. A rectangular prism with edges of 15 cm, 24 cm, and 10 cm.


2. A triangular prism 8 inches high, with a base that is a right triangle with legs
   5 inches and 12 inches long and a hypotenuse 13 inches long.


3. A hexagonal prism 42 cm high with a base that is a regular hexagon with a
   perimeter of 30 cm and an area of 65 square cm.


4. A pentagonal prism, 4 inches high, with a base that is a regular pentagon with
   sides 15 inches long and an area of 387 square inches.


5. A cube 17 cm on each edge.

Volume

Rather than memorizing a lot of different volume formulas, remember that the volume of a prism

is equal to the area of its base times its height. If you use B for the area of the base, V = Bh.

If you need to find the volume of a triangular prism 4 inches high, whose base is an equilateral

triangle with sides 6 inches long, first you’ll need to find the area of the base. Because it is an

equilateral triangle, you can use the 30r-60r-90r triangle relationship to find the height. The

altitude of the equilateral triangle is half the side times the square root of three, or 33. The area

of the triangle is^1

2

1

2

bh63 3 9 3 square inches. Finally, the volume of the prism is the area

of the base times the height, or 934 36 3 cubic inches.

6 in

6 in

6 in

4 in