Volume of Triangular Prisms

NEE

D

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.

03.18.2024 WARM UP

Each shape has a base area of 16
cm2. Calculate the volume of each
shape.
1.

2. A cube that has height of 4 cm.

2.5 cm

Volume of Triangular Prisms

March 18, 2024

Grade 7 Mathematics

12

Lesson Vocabulary

Volume

Triangular Prism

V=Bh

Volume = Base area xheight

cubic units

11

LO:SWBAT solve problems involving the
volume of triangular prisms.

DOL: Given a set of problems, students will
correctly solve problems involving the
volume of triangular prisms in at least 4 of 5
questions.

7.9A solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids.

14

You have learned about the volume of rectangular prisms.
Today we we look at triangular prisms.

What shape is
the base of the

figure?

What other

shapes does a

triangular

prism have?

15

Draymond and Stephanie are debating whether or not the
shapes below are both triangular prisms.
●

Stephanie says they are because they both have parallel bases of a
triangle.

●

Draymond says they are not because the one on the right has a base
of a rectangle not a triangle.

Who is correct?

Open Ended

Draymond and Stephanie are debating whether or not the
shapes below are both triangular prisms.
● Stephanie says they are because they both have parallel bases of a triangle.

• * Draymond says they are not because the one on the right has a base of a rectangle not a triangle.

• Who is correct and why?

16

Now, let’s explore the volume of a triangular prism.
A rectangular prism with dimensions 2 cm by 6 cm by 3 cm
has a volume of 36 cm3. A triangular prism with the same
dimensions has a volume of 18 cm3.

How are their

volumes related?

2 cm

6 cm

3 cm

6 cm

3 cm

17

If you look at your reference chart, the formula for the
volume of a triangular prism is the same as it is for
rectangular prism. Let’s explore.

What is the shape of the base?

What is the formula for base area?

B = base area

h = height of the figure

V = Bh

18

The work for the
volume of two

prisms with same
dimensions using
V=Bh is shown.

What do you
notice in the
example? How is
the formula the
same but the
triangular volume
is the
rectangular
prism?

Rectangular Prism

Triangular Prism

1
2

Open Ended

What do you notice in the example? How is he formula the same but the triangular volume is ½ the rectangular prism?

5 cm

8 cm

4 cm

19

Here is an example.

Solve for volume using V=Bh

Step 1: Write the formula

Step 4: Plug in your values
and solve.

Step 2: Identify the base.
Replace B with the formula
for base area

Step 3: Identify the height
of the figure, h.

21

Now your turn.

Solve for volume using V=Bh

Step 1: Write the formula

Step 4: Plug in your values
and solve.

Step 2: Identify the base.
Replace B with the formula
for base area

Step 3: Identify the height
of the figure, h.

Math Response

What is the volume?

Type answer here

Correct Answer: 135

Deg^°

Rad

Math Response

What is the volume?

Type answer here

Correct Answer: 21

Deg^°

Rad

1.5 cm

7 cm

4 cm

22

Step 1: Write the formula

Step 4: Plug in your values
and solve.

Step 2: Identify the base.
Replace B with the formula
for base area

Step 3: Identify the height
of the figure, h.

Solve for volume using V=Bh

Open Ended

What’s the only difference when solving for volume of a triangular prism versus a 

rectangular prism?

23

Let’s review the activity.

What’s the only difference when solving for

volume of a triangular prism versus a

rectangular prism?

B is base area of a triangle, which is .

You will have to multiply by or divide by 2

when solving for volume of a triangular prism.

bh
2
1
2

Tip: The height
of the figure is
separate from
the height of
the base.
Draw your
own prism.

A triangular prism has a base with a base of
6 cm and a height of 2.5 cm. The height of

the figure is 3 cm. What is the volume?

Can you solve for volume given only words?

24

3 in

2.5 in

6 in

Some of the dimensions of a triangular prism are

shown below. The height of the triangular

prism is 12 cm. What is the volume of the prism

in cubic centimeters?

What’s unique about this problem?

25

5 cm

12 cm

The height is
in the words

Some of the dimensions of a triangular prism are

shown below. The height of the triangular

prism is 12 cm. What is the volume of the prism

in cubic centimeters?

3.2 cm

A triangular prism is pictured.

Jared solves for the volume with his work below.

Is he correct?

26

8 cm

2.6 cm

5 cm

4 cm

Multiple Choice

A triangular prism has a height of 13 inches and a base area of 20 in². Choose the correct volume of the triangular prism in cubic inches.

• 130 in³

• 260 in³

A triangular prism has a height of 13 inches and

a base area of 20 in². Choose the correct

volume of the triangular prism in cubic inches.

Tip: Draw
your own
prism.

Can you solve for volume given only two numbers?

29

A. 130 in3

B. 260 in3

13 in

20 in2

Multiple Choice

A triangular prism has a height of 6 inches and a base area of 18 in². What is the volume of the triangular prism in cubic inches?

• 24 in³

• 486 in³

• 54 in³

• 108 in³

A triangular prism has a height of 6 inches
and a base area of 18 in2. What is the volume

of the triangular prism in cubic inches?

A. 24 in3

B. 486 in3

C. 54 in3

D. 108 in3

30

6 in

18 in2

31

Solve for the height if the volume is 144 ft3.

Step 1: Write the formula

Step 4: Plug in your values
and solve.

Step 2: Identify the base.
Replace B with the formula
for base area

Step 3: Identify the
dimensions you know.

What if the right side
wasn’t divisible by 2?

3 ft

8 ft

?