Rectangular Pyramid Surface Area

NEED

DO

VOICE LEVEL 0.
Complete WARM UP
(Question on the
board). Use the mini
whiteboard to write
your answer.

THEN

Be ready to share
your responses to
class.

03.28.2024 WARM UP

Calculate the area of the shape
below.

4.2 in

4 in

1.25 in

Dropdown

The area area of the triangle on the left is ​

Select answer

.

The area of the triangle on the right is ​ ​

Select answer

​

Surface Area of Rectangular Pyramids

March 28, 2024

Grade 7 Mathematics

3

LO:SWBAT solve problems involving the lateral
and total surface area of a rectangular pyramid
by determining the area of the shape's net.

DOL: Given a set of problems, students will
correctly solve problems involving lateral and
total surface area of rectangular pyramids in at
least 4 of 5 questions.

MATH.7.9D Solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular
prism, and triangular pyramid by determining the area of the shape’s net.

4

Lesson Vocabulary

Net

Lateral Surface Area

Two-dimensional

representation of a 3D figure.

Area of the lateral faces
Measured in square units

5

Lesson Vocabulary

Net

Total Surface Area

Two-dimensional

representation of a 3D figure.

Area of the lateral faces AND base

Measured in square units

6

We’ve practiced solving for the area of complex shapes.
Some of the complex shapes we’ve seen are nets of 3D
figures.

Which 3D figure
does the net on

the left represent?
How do you know?

7

The total space covering the outside of a figure is called
surface area.

Which units will be

used to find the surface

area of a 3D shape?

8

Some situations
require you to
cover the entire
outside of a 3D

shape.

Can you think of

any situations

where you

wouldn’t cover
the base of a
rectangular
pyramid?

Lateral Surface Area

Total Surface Area

Area of ONLY the Area of all faces
non-base faces

Architecture
Roof Designs

9

Let’s begin by determining the lateral surface area of
rectangular pyramid.

Which colors would make

up the non-base faces?

Of those, how many pairs
of congruent shapes do

you see?

Categorize

Options (2)

Blue

Red

Organize these options into the right categories

Non bases

Bases

10

Today we will also determine the total surface area of
rectangular pyramids.

How will this be different
from lateral surface area?

In total, for how many

faces will you calculate the

area?

11

Which triangles are

congruent?

5 cm

7 cm

For every rectangular pyramid, there will be 4 non-base
faces. Solve for the combined area of them to solve for

lateral surface area.

2

3

4

4 cm

4 cm

1

Match

Match the following

• Triangle 1 is congruent with

• Triangle 2 is congruent with

• Congruent means

Triangle 3

Triangle 4

Equal

• Triangle 3

• Triangle 4

• Equal

12

Draw and label four triangles. It helps to group the pairs.

Label the dimensions. Calculate the area of each one.

5 cm

7 cm

2

3

4

4 cm

4 cm

1

Draw

Draw and label four triangles. It helps to group the pairs. Label the dimensions. Calculate the area of each one.

Math Response

The lateral surface area is.....

Type answer here

Correct Answer: 48

Deg^°

Rad

Draw

Draw and label four triangles. It helps to group the pairs. Label the dimensions. Calculate the area of each one.

Math Response

The total surface area is.....

Type answer here

Correct Answer: 93

Deg^°

Rad

17

Lateral Surface Area

Step 1: Identify the
non-base faces.

Step 4: Add to find the
desired area.

Step 2: Draw and label
each shape separately.
Write their area formulas.

Step 3: Plug in your values
and solve.

Now your turn.

6 cm

5 cm

4 cm

4 cm

2

3

4

1

Math Response

The total surface area is.....

Type answer here

Correct Answer: 75

Deg^°

Rad

Let’s mix it all up and practice!

Bulb by Kaja Gierschek from Pixabay

Multiple Choice

A box shaped like a cube is being painted yellow. The box’s base will be cut out. What is the area that will be painted in ft²?

• 192

• 48

• 24

• 96

A box shaped like a cube is being painted
yellow. The box’s base will be cut out. What

is the area that will be painted in ft2?

A. 192 ft2

B. 48 ft2

C. 24 ft2

D. 96 ft2

20

Tip: What does
a square base
mean about the
dimensions?

Multiple Choice

Paul unfolded a pyramid container and wants to finds the area of just the white label. What is the area of the unshaded part in ft²?

• 6

• 18

• 12

• 24

Which is greater?

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A

B

Select a net. Each one is a rectangular pyramid with a

square base. Calculate the indicated surface area.

8 ft

7 ft

9 ft

Total

Surface Area

7 ft

12 ft

Lateral

Surface Area

Paul unfolded a pyramid container and wants
to finds the total surface area. What is the area

in square feet?

A. 6 ft2

B. 28 ft2

C. 12 ft2

D. 24 ft2

23

Tip: Which
shapes are the
non-base
faces?

1.5 ft

4 ft

4 ft

24

The net of a rectangular pyramid is shown below. What is
the lateral surface area of the prism in square centimeters?

A. 75 cm2

B. 136.25 cm2

C. 155 cm2

D. 80 cm2

10 cm

7.5 cm

8 cm

A. The lateral surface area of the tent

is 56 ft2

B. The lateral surface area of the tent

is 140 ft2

C. The total surface area of the tent

is 239 ft2

D. The total surface area of the tent

is 323 ft2

A tent is built in the shape of a rectangular pyramid.
Select TWO statements that are true about the tent.

25

8 ft

9 ft

7 ft

11 ft

A road sign is being painted yellow. The

paint will cover all the faces. What is the total

area that will be painted in square feet?

A. 96 ft2

B. 248 ft2

C. 336 ft2

D. 960 ft2

26

Tip: What does
a square base
mean about the
dimensions?

A. 126 ft2

B. 90 ft2

C. 270 ft2

D. 180 ft2

28

Alan is making a cardboard structure for his children to play

in. How many square feet of cardboard in total?

A. 112 ft2

B. 144 ft2

C. 98 ft2

D. 242 ft2

A roof is built on a shed in the shape of a
rectangular pyramid. The base will not be

covered. What is the lateral surface area in ft2?

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7 ft

7 ft

7 ft

9 ft

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The net of a rectangular pyramid is shown below. What is
the total surface area of the prism in square centimeters?

A. 62.25 cm2

B. 20.25 cm2

C. 100.5 cm2

D. 189 cm2

7 cm

4.5 cm

6 cm

Consider the surface area questions from the previous slides.

How can you use the problem to

determine if you are solving for lateral

surface area?

Words and phrases such as “sides”, “no base”,

“lateral”, “non-base faces” mean lateral surface area.

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