Name ———————————————————————
LESSON
12.1
Date ————————————
Practice A
For use with pages 824–833
Describe the solid. If it is a polyhedron, find the number of faces, vertices,
and edges.
1.
2.
3.
Use Euler’s Theorem to find the value of n.
4. Faces: n
5. Faces: 5
LESSON 12.1
6. Faces: 8
Vertices: 6
Edges: n
Vertices: 8
Edges: 12
Vertices: n
Edges: 18
Sketch the polyhedron.
7. Cube
8. Rectangular prism
9. Trapezoidal pyramid
388
10.
11.
12.
13.
14.
15.
Geometry
Chapter 12 Resource Book
Copyright © Holt McDougal. All rights reserved.
Identify the solid. Find the number of faces, vertices, and edges.
Check your answer using Euler’s Theorem.
Name ———————————————————————
LESSON
12.1
Practice A
For use with pages 824–833
continued
Date ————————————
LESSON
0.0
Determine whether the solid is convex or concave.
16.
17.
18.
Identify and sketch the cross section. Then find its perimeter (or
circumference) and area.
19.
20.
21.
CM
CM
FT
IN
LESSON 12.1
FT
IN
In Exercises 22–25, determine whether the statement is true or false.
22. A polyhedron can have a circular face.
23. A polyhedron can have an equal number of faces and vertices.
24. The cross section of a cube could be an equilateral triangle.
Copyright © Holt McDougal. All rights reserved.
25. The cross section of a square pyramid could be a triangle.
26. Sketch an example of a solid that is not a polyhedron. Do not use a cone, cylinder,
or sphere.
Geometry
Chapter 12 Resource Book
389
Lesson 12.1
Practice Level A
7.
8.
7.
8.
ANSWERS
1. The solid has a curved surface, so it is not a
polyhedron.
2. The solid is formed by polygons, so it is a
polyhedron. The two bases are congruent trapezoids, so it is a trapezoidal prism. It has 6 faces,
consisting of 2 trapezoidal bases and 4 rectangular
faces. It has 8 vertices and 12 edges.
3. The solid has a curved surface, so it is not a
polyhedron.
4. 6 5. 9 6. 12
2. The solid has a curved surface, so it is not a
polyhedron.
3. The solid has a curved surface, so it is not a
polyhedron.
4. 4 5. 16 6. 36
9.
10. rectangular pyramid; 5, 5, 8
11. rectangular prism; 6, 8, 12
9.
12. triangular prism; 5, 6, 9
13. hexagonal pyramid; 7, 7, 12
14. hexagonal prism; 8, 12, 18
15. non-regular pentagonal prism; 7, 10, 15
10. triangular prism; 5 faces, 6 vertices, 9 edges
11. rectangular prism; 6 faces, 8 vertices, 12 edges
Copyright © Holt McDougal. All rights reserved.
12. pentagonal pyramid; 6 faces, 6 vertices,
10 edges
13. non-regular hexagonal prism; 8 faces,
12 vertices, 18 edges
14. trapezoidal prism; 6 faces, 8 vertices, 12 edges
15. non-regular, concave prism; 8 faces,
12 vertices, 18 edges
16. convex 17. concave 18. convex
19. Check sketches; triangle with base 4 cm and
height 3 cm; P 5 12 cm; A 5 6 cm2.
20. Check sketches; square with sides 6 in.;
P = 24 in.; A 5 36 in.2.
21. Check sketches; rectangle with length 10 ft
and width 5 ft; P 5 30 ft; A 5 50 ft2.
22. false 23. true 24. true
25. true 26. Sample answer:
Practice Level B
1. The solid is formed by polygons, so it is a
polyhedron. The two bases are congruent
rectangles, so it is a rectangular prism. It has
6 faces, 8 vertices and 12 edges.
16. octagon 17. concave
18. convex 19. concave
20. Check sketches; regular pentagon with sides
3 cm; P 5 15 cm; A ø 15.5 cm2.
21. Check sketches; circle with radius 5 ft; C ø
31.4 ft; A ø 78.5 ft2.
}
22. Check sketches; rectangle with length 7Ï 2 m
and width 7 m; P ø 33.8 m; A ø 69.3 m2.
23. B
24. rectangular prism and rectangular pyramid;
}
9 faces 25. equilateral 26. Ï2 27. 24
Practice Level C
1. The solid is formed by polygons, so it is a
polyhedron. The base is a heptagon, so it is a
heptagonal pyramid. It has 8 faces, consisting of
1 base, 5 visible triangular faces, and 2 non-visible
triangular faces. The polyhedron has 8 vertices
and 14 edges.
2. The solid has a curved surface, so it is not a
polyhedron.
3. The solid is formed by polygons, so it is a
polyhedron. The two bases are congruent nonagons,
so it is a nonagonal prism. It has 11 faces,
consisting of 2 nonagonal bases and 9 rectangular
faces. It has 18 vertices and 27 edges.
4. 6 5. 36 6. 54
Geometry
Chapter 12 Resource Book
A57