Here are the steps to find the volume of a triangular pyramid: 1. Identify the base of the pyramid. For a triangular pyramid, the base will be a triangle. Measure the base dimensions. 2. Measure the height of the pyramid from the vertex perpendicular to the base. 3. Use the formula: Volume (V) = (1/3) x Base Area (B) x Height (h) 4. Find the area of the triangular base using 1/2 x base x height or another appropriate formula. 5. Plug the values into the volume formula: V = (1/3) x B x h 6. Simplify and calculate the volume.

1. Use the solve a simpler problem strategy to solve Exercises 1–3.
1. Mr. Cole decided to build a deck around his swimming pool. His pool is
25 feet by 10 feet. He wants the deck to be 2.5 feet wide. What will the
area of the deck be?
2. Over the weekend, Darrell spent $68. Of that, about 71% was spent on
a game. How much money was NOT spent on a game?
3. Becky can make 6 bracelets in 3 days. How many bracelets can she
and two friends make in 8 days working at the same rate?
4. The graph shows the results of
the 2008 Summer Olympics. The
U.S. received a total of 110 medals.
About how many were gold?
Course 2, Lesson 8-5

2. Course 2, Lesson 8-5
ANSWERS
1. 200 ft²
2. $19.72
3. 48
4. 36

3. Geometry
Course 2, Lesson 8-5
HOW do measurements help you
describe real-world objects?

4. Course 2, Lesson 8-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Geometry
• 7.G.6
Solve real-world and mathematical problems involving area,
volume and surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons, cubes, and right
prisms.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
6 Attend to precision.

5. • To find the volume of a pyramid
• To find the height of a pyramid
Course 2, Lesson 8-5
Geometry

6. Course 2, Lesson 8-5
Geometry
• pyramid
• lateral face

7. Course 2, Lesson 8-5
Geometry
Words The volume V of a pyramid Model
is one third the area of the
base B times the height of
the pyramid h.
Symbols V = Bh
1
3

8. 1
Need Another Example?
2
3
4
Step-by-Step Example
1. Find the volume of the pyramid.
Round to the nearest tenth.
V = Bh
The volume is about 4.2 cubic inches.
V = (3.2 • 1.4) 2.8
Volume of a pyramid
B = 3.2 • 1.4, h = 2.8
V ≈ 4.2 Simplify.

9. Answer
Need Another Example?
Find the volume of a pyramid that has a height of
3.3 inches and a rectangular base with a length of
4.2 inches and a width of 2.1 inches. Round to the
nearest tenth.
9.7 in3

10. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. Find the volume of the pyramid.
Round to the nearest tenth.
V = Bh
The volume is about 95.0 cubic meters.
V = • 8.1 • 6.4 11
Volume of a pyramid
B = • 8.1 • 6.4, h = 11
V = 95.04 Simplify.

11. Answer
Need Another Example?
Find the volume of the pyramid.
Round to the nearest tenth.
119.2 ft3

12. Need Another Example?
Step-by-Step Example
3. The rectangular pyramid shown has a
volume of 90 cubic inches. Find the
height of the pyramid.
1
2
3
4
5
6
V = Bh
The height of the pyramid is 6 inches.
90 = (9 • 5)h
Volume of a pyramid
V = 90, B = 9 • 5
90 = 15h Multiply.
Divide by 15.
6 = h Simplify.

13. Answer
Need Another Example?
The triangular pyramid shown has a volume of
110 cubic centimeters. What is the height of the
pyramid?
6 cm

14. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
4. A triangular pyramid has a volume of
44 cubic meters. It has an 8-meter
base and a 3-meter height. Find the
height of the pyramid.
V = Bh
The height of the pyramid is 11 meters.
44 = • 8 • 3 h
Volume of a pyramid
V = 44, B = • 8 • 3
44 = 4h Multiply.
Divide by 4.
11 = h Simplify.

15. Answer
Need Another Example?
A triangular pyramid has a volume of 12 cubic inches.
The triangular base has a 4-inch base and a 3-inch
height. Find the height of the pyramid.
6 in.

16. 1
Need Another Example?
2
3
4
Step-by-Step Example
5. Kamilah is making a model of the
Food Guide Pyramid for a class
project. Find the volume of the square
pyramid.
V = Bh
The volume is 576 cubic inches.
V = (12 • 12)12
Volume of a pyramid
B = 12 • 12, h = 12
V = 576 Multiply.

17. Answer
Need Another Example?
A scale model of an Egyptian pyramid is shown.
Find the volume of the square pyramid.
216 in3

18. How did what you learned
today help you answer the
Course 2, Lesson 8-5
Geometry
HOW do measurements help you
describe real-world objects?

19. How did what you learned
today help you answer the
Course 2, Lesson 8-5
Geometry
HOW do measurements help you
describe real-world objects?
Sample answers:
• To find the volume of a pyramid-shaped figure, such as
a building
• To find the height of a pyramid-shaped figure when you
know its volume

20. Write the steps that you
would use to find the
volume of a triangular pyramid.
Course 2, Lesson 8-5
Ratios and Proportional RelationshipsFunctionsGeometry