Page 256 - ABCTE Study Guide_Neat

Question

What is the surface area of a square pyramid with sides of 4 cm and the faces measuring 5.5 cm in
height?

Round your answer to the nearest square centimeter.

2
A 44 cm

2
B 52 cm

2
C 60 cm

2
D 104 cm

Answer

Choice C is the correct answer. The surface area of the pyramid is the sum of the areas of its polygonal
faces. The pyramid has a square base with sides 4 cm long, so its area is . The
pyramid has four triangular faces, each with base 4 cm and height 5.5 cm. Each triangular face has

area , so the sum of the areas of the four triangular faces is .
2
The surface area of the pyramid is , or 60 cm .

Volume

A general formula for the volume of a prism is , where B is the area of the base and h is the height.

3
Since volume is three-dimensional, it is expressed in cubic units, like cubic inches (in ), cubic centimeters
3
3
(cm ), and cubic feet (ft ).

Let’s look back at the prism from the previous section. What is its volume?

The bases are any pair of congruent faces; this prism has three pairs of congruent faces. We’ll let the
faces with dimensions 8 in. x 12 in. be the bases, since they are on the top and bottom (and that’s where
we like our bases).