Spatial Reasoning

Any Question Type: Measure to Solve Problems
On some tests, you may have to measure a figure in order to answer a question. Pay
close attention to the units of measure asked for in the question. Some questions
ask you to measure to the nearest centimeter, and some ask you to measure to the
nearest inch.
Multiple Choice: The net of a square pyramid is shown below.
Use a ruler to measure the dimensions of the pyramid to
the nearest centimeter.
Which of the following best represents the
total surface area of the square pyramid?
9 square centimeters
21 square centimeters
33 square centimeters
36 square centimeters
Use a centimeter ruler to measure one side
of the square base. The measurement
to the nearest centimeter is 3 cm.
The base is a square, so all four side
lengths are 3 cm.
Measure the altitude of a triangular face,
which is the slant height of the pyramid.
The altitude is 2 cm. Label the drawing
with the measurements.
To find the total surface area of the pyramid,
find the base area and the lateral area.
The base of the pyramid is a square.
The base area of the pyramid is A = s 2 = (3) 2 = 9 cm 2 .
The area of one triangular face is A = _ 1 2 bh = _ 1 2 (3)(2) = 3 cm 2 .
The pyramid has 4 faces, so the lateral area is 4 (3) = 12 cm 2 .
The total surface area is 9 + 12 = 21 cm 2 . The correct answer choice is B.
736 Chapter 10 Spatial Reasoning