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Lanier Middle School
“An International Baccalaureate Middle Years Programme School”
7th – LESSON 10.3 Lateral and Total Surface Area
Daily Objective: How do you find the Lateral and Total Surface Area of Rectangular & Triangular Prisms and Pyramids?
The lateral faces of a prism are parallelograms that connect the
bases. Each face that is not a base is a lateral face. The sum of
the areas of all the lateral faces is the lateral area of the prism.
The surface area is the sum of the areas of all of the surfaces of a
figure expressed in square units. The total surface area of a prism
can be found by finding the sum of the lateral area and the area of
the bases.
A net of a rectangular prism is shown. Use the net to find the
lateral area and the total surface area of the solid. Each square
represents one square inch.
A. Identify the prism.
B. Label the faces of the prism
C. Determine the Lateral Area
D. Calculate the Total Surface Area
Use the net on the right to find the Lateral Area and the Total
Surface Area of the solid represented by the net.
A. Identify the solid.
B. Label the faces of the solid.
C. Determine the Lateral Area.
D. Calculate the Total Surface Area.
Shoshanna’s team plans to build stand to display sculptures. Each
stand will be in the shape of a rectangular prism. The prism
willhave a square base with side lengths of 2.5 feet, and it will be
3.5 feet high. The team plans to cover the stands with metallic
foil that costs $0.22 per square feet. How much money will the
team save on each stand if they cover only the lateral area instead
of the total surface area?
Make a sketch of this prism on your notebook followed
by your calculations.
Lanier Middle School
“An International Baccalaureate Middle Years Programme School”
Use the net of this rectangular pyraid to find the Lateral
Area and the Total Surface Area of this pyramid.
Identify the Base and Lateral Faces.
In the rectanglar pyramid shown on the right, the base is a
rectangle, and the lateral faces are triangles. The Lateral Area and
the Total Surface Area are defined in the same way as they are for
a prism.
The base and all three faces of a triangular pyramid are equilateral
triangles with side lengths of 3 feet. The height of each triangle is
2.6 feet. Use the net to find the Lateral Area and the Total Surface
Area of the trianglar pyramid.
Draw a net for the pyramid shown below and find the
Lateral Area and the Total Surfae Area of the pyramid.
Kwame’s team will make two triangular pyramids to decorate the
entrance to an exhibit. They will be wrapped in the same metallic
foil. Each base is an equilateral triangle. If the base has an area of
about 3.9 square feet, how much will the team save altogether by
covering only the lateral area of the two pyramids?
The foil costs $0.22 per square foot.
A triangular prism is shown below.
A three dimensional figure is shown sitting on a base.
1
2
3
Sketch a net of the figure in your composition book.
Calculate the Lateral Area of the prism.
Calculate the Total Surface Area.
7 Draw a net of the prism in your notebook.
8 Find the Lateral Area of the prism.
9 Find the Total Surface Area of the prism.
10 Draw a net in your notebook to find the Total Surface
Area of the pyramid shown below. Then find the cost of
wrapping the pyramid completely in gold foil that costs
$0.05 per square centimeter.
Lanier Middle School
“An International Baccalaureate Middle Years Programme School”
12 Draw a net to find the Lateral Area and the Total Surface Area
of the cereal box.
13 Describe a net for the shipping carton for number 12.
14 A shiping carton is in the shape of a triangular prism. Draw a
net to find the Lateral Area and the Total Surface Area of the
carton.
15 Victor wrapped this gift box with adhesive paper (with no
overlap). Howmuch paper did he use?
16 Name a three-dimensional shape that has four triangular faces
and one rectangular face.
17 Cindi wants to cover the top and sides of this box with glass
tiles that are 1 cm square. How many tiles will she need?
18 A glass paperweight has the shape of a triangular prism. The
bases are equilateral triangles with side lenghts of 4 inches and
heights of 3.5 inches. The height of the prism is 5 inches. Find the
Lateral Area and the Total Surface Area of the paperweight.
Draw a net in your notebook to help you with the calculations.
19 The doghouse shown has a floor, but no windows. Find the
total surface area of the doghouse (including the door).
20 Describe the simplest way to find the Total Surface
Area of a cube.
21 Describe how you approach a problem involving
Lateral Area and Total Surface Area. What do you do
first? In what ways can you use the figure that is given
with a problem? What are some shortcuts that you
might use when you are calculating these areas?
22 A pedestal in a craft store is in the shape of a
triangular prism. The bases are right triangles with side
lengths of 12 cm, 16 cm, and 20 cm. The store owner
used 192 square centimeters of burlap cloth to cover the
Lateral Area of the pedestal. Find the height of the
pedestal.
23 The base of Prism A has an area of 80 square feet, and
the base of Prism B has an area of 80 square feet. The
height of Prism A is the same as the height of Prism B. Is
the base of Prism A congruent to the base of Prism B?
Explain.
24 A triangular pyramid is made of 4 equilateral
triangles. The sides of the triangles measure 5 meters,
and the height of each triangle is 4.3 m. A rectangular
prism has a height of 4.3 m and a square base that is 5 m
on each side. Susan says that the Total Surface Area of
the prism is more than twie the Total Surface area of the
pyramid. Is she correct? Explain.