Download Lateral and Surface Area of Right Prisms

CHAPTER 11
A
You will need
Lateral and Surface
Area of Right Prisms
• a ruler
• a calculator
c GOAL
Calculate lateral area and surface area of right prisms.
Learn about the Math
A prism is a polyhedron (solid whose faces are polygons)
whose bases are congruent and parallel. When trying to
identify a right prism, ask yourself if this solid could have
been created by placing many congruent sheets of paper on
top of each other. If so, this is a right prism. Some examples
of right prisms are shown below.
Triangular prism
right prism
prism that has bases
aligned one above the
other and has lateral
faces that are
rectangles
Rectangular prism
The surface area of a right prism can be calculated using
the following formula: SA 5 2B 1 hP, where B is the area of
the base, h is the height of the prism, and P is the perimeter
of the base.
The lateral area of a figure is the area of the non-base faces
only. When a prism has its bases facing up and down, the
lateral area is the area of the vertical faces. (For a rectangular
prism, any pair of opposite faces can be bases.) The lateral
area of a right prism can be calculated by multiplying the
perimeter of the base by the height of the prism. This is
summarized by the formula: LA 5 hP.
Copyright © 2009 by Nelson Education Ltd.
Reproduction permitted for classrooms
lateral area
area of the non-base
faces of a figure
11A Lateral and Surface Area of Right Prisms
1
Jorge is trying to wrap a present that is in a box shaped as a
right prism. He wants to determine the surface area and lateral
area of the prism to see if he has enough wrapping paper to
cover the entire box or only the vertical faces of the box. The
drawing below shows the dimensions of the present.
1.50 m
1.00 m
0.25 m
can Jorge calculate the surface area
? How
and lateral area of this right prism?
A. Calculate the area of the base of the prism.
B. Calculate the perimeter of the base of the prism.
C. Use your calculations from parts A and B along with the
height of the prism to calculate the total surface area.
Use the following formula as a guide for your
calculation: SA 5 2B 1 hP.
D. Use the formula, LA 5 hP to calculate the lateral area of
this prism.
E. If Jorge has 1.50 m2 of paper, would he have enough to
cover the entire box or only the vertical faces of the box?
Reflecting
1. What information do you need to have about a right prism
to calculate its surface area?
2. How do the surface area of a prism and the lateral area of
a prism differ?
3. Is the lateral area of a right prism ever larger than the
surface area?
2
Nelson Mathematics Secondary Year Two, Cycle One
Reproduction permitted for classrooms
Copyright © 2009 by Nelson Education Ltd.
Work with the Math
Example 1: Calculating the surface area
of a right prism
Use the dimensions of the right prism shown below to calculate its surface
area.
3.0 cm
3.0 cm
4.0 cm
2.6 cm
3.0 cm
Emilio’s Solution
First, I will calculate the surface area of this right prism. To do this I must
first calculate the area and perimeter of the base of the prism. I will then use
the formula SA 5 2B 1 hP to calculate the surface area.
The area of the base can be found by using the formula for the area
1
of a triangle, 2 bh.
1
(3.0 cm)(2.6 cm) 5 3.9 cm2
2
The perimeter of the base can be found by adding the length of each segment
forming the triangular bases. P 5 3.0 cm 1 3.0 cm 1 3.0 cm; P 5 9.0 cm
I know the height of this prism is 4.0 cm.
I can now substitute the area of the base into the formula for B, the perimeter
of the base for P, and the height of the prism for h.
I will simplify to determine the total surface area for this right prism.
SA 5 2(3.9 cm2) 1 4.0 cm (9.0 cm) 5 43.8 cm2
The surface area is 43.8 cm2.
Copyright © 2009 by Nelson Education Ltd.
Reproduction permitted for classrooms
11A Lateral and Surface Area of Right Prisms
3
A
Checking
4. Calculate the surface area and lateral
area of the right prism shown.
6. Determine the surface area of each of
the following right prisms.
a)
10 mm
10 cm
15 mm
10 mm
2 cm
B
3 cm
Practising
5. Complete each of the following
statements with a term that will make
it a true statement.
a) A
is a prism
that has bases aligned one above
the other and has lateral faces that
are rectangles.
b) The
of a
figure is the area of the non-base
faces only.
c) The
of a
figure is equal to the height of the
prism multiplied by the perimeter of
its base.
b)
2.00 m
2.00 m
3.00 m
1.32 m
3.00 m
c)
12 cm
4 cm
10 cm
d)
3.00 m
3.00 m
1.66 m
5.00 m
5.00 m
4
Nelson Mathematics Secondary Year Two, Cycle One
Reproduction permitted for classrooms
Copyright © 2009 by Nelson Education Ltd.
7. Determine the surface area and
lateral area of each of the following
right prisms.
a)
1 cm
1 cm
4 cm
b)
4.00 mm
4.00 mm
3.00 mm
1.94 mm
7.00 mm
c)
14 cm
8 cm
28 cm
d)
1 mm
1 mm
11 mm
e)
25 cm
9 cm
6 cm
Copyright © 2009 by Nelson Education Ltd.
Reproduction permitted for classrooms
11A Lateral and Surface Area of Right Prisms
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