501 Geometry Questions

Types of Prisms

You investigated rectangular and cubic prisms, among others, in the last
chapter. All the three-dimensional polygons you studied in chapter 14 are
known as right prisms. The sides of a right prismperpendicularly meet the
base to form a 90° angle. Remember that the baseis the polygon that
defines the shape of the solid.

The Volume of a Right Prism

Given anyright prism, if you can calculate the area of one of its congruent
bases, then multiply that area by the height of the prism, you will find its
volume. In the following figure, the shaded triangular base on the right side
of the prism has an area of ^12 (9)(12) = 54 cm^2. If this area is multiplied by
the “height” of the prism, which is the 18 cm edge, then that will yield a
total volume of 972 cm^3. This method can be used with any right prism.

18 cm

12 cm

Volume = (area of triangular base) (height)

V = [(  ) (9)(12)]  (18)

V = 54 cm^3

9 cm

base base base

Right Triangular

Prism

Right Rectangular

Prism

Right Pentagonal

Prism

501 Geometry Questions