Glencoe Math Accelerated, Student Edition
1st Edition
ISBN: 9780076637980
Author: McGraw-Hill Glencoe
Publisher: MCG
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Question
Chapter 12.4, Problem 21IP
(a)
To determine
To complete: The table.
(a)
Expert Solution
Answer to Problem 21IP
The complete table is given below.
Explanation of Solution
Given information:
Consider the given table.
| Name | Triangular
Pyramid | Square
Pyramid | Pentagonal
Pyramid |
| Vertices | 4 | 5 | |
| Faces | 6 | ||
| Edges | 8 |
Calculation:
A triangular pyramid is a three-dimensional closed shape that 4 vertices, 4 faces, and 6 edges.
A square pyramid is a three-dimensional closed shape that 5 vertices, 5 faces, and 8 edges.
A pentagonal pyramid is a three-dimensional closed shape that 6 vertices, 6 faces, and 10 edges.
Complete the table.
| Name | Triangular Pyramid | Square Pyramid | Pentagonal Pyramid |
| Shape |  |  |  |
| Vertices | 4 | 5 | 6 |
| Faces | 4 | 5 | 6 |
| Edges | 6 | 8 | 10 |
Conclusion:
Therefore, the complete table is shown above.
(b)
To determine
To analyze: The relation between the vertices, faces, and edges.
(b)
Expert Solution
Answer to Problem 21IP
The number of vertices and number of faces in each shape is similar. Moving from left to right, the edges of each shape is increased by 2 and the vertices are increased by 1.
Explanation of Solution
Given information:
Consider the given table.
| Name | Triangular Pyramid | Square Pyramid | Pentagonal Pyramid |
| Shape |  |  |  |
| Vertices | 4 | 5 | 6 |
| Faces | 4 | 5 | 6 |
| Edges | 6 | 8 | 10 |
Calculation:
From part (a), the number of vertices and number of faces in each shape is similar. Moving from left to right, the edges of each shape is increased by 2 and the vertices are increased by 1.
Conclusion:
Therefore, the number of vertices and number of faces in each shape is similar. Moving from left to right, the edges of each shape is increased by 2 and the vertices are increased by 1.
(c)
To determine
To write: An equation that compares the number of vertices and the number of faces to number of edges.
(c)
Expert Solution
Answer to Problem 21IP
The required equation is
Explanation of Solution
Given information:
Consider the given table.
| Name | Triangular Pyramid | Square Pyramid | Pentagonal Pyramid |
| Shape |  |  |  |
| Vertices | 4 | 5 | 6 |
| Faces | 4 | 5 | 6 |
| Edges | 6 | 8 | 10 |
Calculation:
From part (a), the number of vertices and number of faces in each shape is similar. Moving from left to right, the edges of each shape is increased by 2 and the vertices are increased by 1.
Let the number of vertices is
Conclusion:
Therefore, the required equation is
Chapter 12 Solutions
Glencoe Math Accelerated, Student Edition
Ch. 12.1 - Prob. 1GPCh. 12.1 - Prob. 2GPCh. 12.1 - Prob. 3GPCh. 12.1 - Prob. 4GPCh. 12.1 - Prob. 5GPCh. 12.1 - Prob. 6GPCh. 12.1 - Prob. 7IPCh. 12.1 - Prob. 8IPCh. 12.1 - Prob. 9IPCh. 12.1 - Prob. 10IP
Ch. 12.1 - Prob. 11IPCh. 12.1 - Prob. 12IPCh. 12.1 - Prob. 13IPCh. 12.1 - Prob. 14IPCh. 12.1 - Prob. 15IPCh. 12.1 - Prob. 16IPCh. 12.1 - Prob. 17IPCh. 12.1 - Prob. 18IPCh. 12.1 - Prob. 19IPCh. 12.1 - Prob. 20IPCh. 12.1 - Prob. 21IPCh. 12.1 - Prob. 22IPCh. 12.1 - Prob. 23IPCh. 12.1 - Prob. 24IPCh. 12.1 - Prob. 25HPCh. 12.1 - Prob. 26HPCh. 12.1 - Prob. 27HPCh. 12.1 - Prob. 28HPCh. 12.1 - Prob. 29HPCh. 12.1 - Prob. 30STPCh. 12.1 - Prob. 31STPCh. 12.1 - Prob. 32STPCh. 12.1 - Prob. 33STPCh. 12.1 - Prob. 34CCRCh. 12.1 - Prob. 35CCRCh. 12.1 - Prob. 36CCRCh. 12.1 - Prob. 37CCRCh. 12.1 - Prob. 38CCRCh. 12.1 - Prob. 39CCRCh. 12.1 - Prob. 40CCRCh. 12.1 - Prob. 41CCRCh. 12.1 - Prob. 42CCRCh. 12.1 - Prob. 43CCRCh. 12.1 - Prob. 44CCRCh. 12.1 - Prob. 45CCRCh. 12.1 - Prob. 46CCRCh. 12.1 - Prob. 47CCRCh. 12.1 - Prob. 48CCRCh. 12.2 - Prob. 1GPCh. 12.2 - Prob. 2GPCh. 12.2 - Prob. 3GPCh. 12.2 - Prob. 4GPCh. 12.2 - Prob. 5GPCh. 12.2 - Prob. 6GPCh. 12.2 - Prob. 7GPCh. 12.2 - Prob. 8IPCh. 12.2 - Prob. 9IPCh. 12.2 - Prob. 10IPCh. 12.2 - Prob. 11IPCh. 12.2 - Prob. 12IPCh. 12.2 - Prob. 13IPCh. 12.2 - Prob. 14IPCh. 12.2 - Prob. 15IPCh. 12.2 - Prob. 16IPCh. 12.2 - Prob. 17IPCh. 12.2 - Prob. 18IPCh. 12.2 - Prob. 19IPCh. 12.2 - Prob. 20IPCh. 12.2 - Prob. 21IPCh. 12.2 - Prob. 22IPCh. 12.2 - Prob. 23IPCh. 12.2 - Prob. 24IPCh. 12.2 - Prob. 25IPCh. 12.2 - Prob. 26IPCh. 12.2 - Prob. 27IPCh. 12.2 - Prob. 28IPCh. 12.2 - Prob. 29HPCh. 12.2 - Prob. 30HPCh. 12.2 - Prob. 31HPCh. 12.2 - Prob. 32HPCh. 12.2 - Prob. 33HPCh. 12.2 - Prob. 34STPCh. 12.2 - Prob. 35STPCh. 12.2 - Prob. 36STPCh. 12.2 - Prob. 37STPCh. 12.2 - Prob. 38CCRCh. 12.2 - Prob. 39CCRCh. 12.2 - Prob. 40CCRCh. 12.2 - Prob. 41CCRCh. 12.2 - Prob. 42CCRCh. 12.2 - Prob. 43CCRCh. 12.2 - Prob. 44CCRCh. 12.2 - Prob. 45CCRCh. 12.2 - Prob. 46CCRCh. 12.2 - Prob. 47CCRCh. 12.2 - Prob. 48CCRCh. 12.2 - Prob. 49CCRCh. 12.2 - Prob. 50CCRCh. 12.2 - Prob. 51CCRCh. 12.3 - Prob. 1GPCh. 12.3 - Prob. 2GPCh. 12.3 - Prob. 3GPCh. 12.3 - Prob. 4GPCh. 12.3 - Prob. 5GPCh. 12.3 - Prob. 6IPCh. 12.3 - Prob. 7IPCh. 12.3 - Prob. 8IPCh. 12.3 - Prob. 9IPCh. 12.3 - Prob. 10IPCh. 12.3 - Prob. 11IPCh. 12.3 - Prob. 12IPCh. 12.3 - Prob. 13IPCh. 12.3 - Prob. 14IPCh. 12.3 - Prob. 15IPCh. 12.3 - Prob. 16IPCh. 12.3 - Prob. 17IPCh. 12.3 - Prob. 18IPCh. 12.3 - Prob. 19IPCh. 12.3 - Prob. 20IPCh. 12.3 - Prob. 21IPCh. 12.3 - Prob. 22IPCh. 12.3 - Prob. 23HPCh. 12.3 - Prob. 24HPCh. 12.3 - Prob. 25HPCh. 12.3 - Prob. 26HPCh. 12.3 - Prob. 27STPCh. 12.3 - Prob. 28STPCh. 12.3 - Prob. 29STPCh. 12.3 - Prob. 30STPCh. 12.3 - Prob. 31CCRCh. 12.3 - Prob. 32CCRCh. 12.3 - Prob. 33CCRCh. 12.3 - Prob. 34CCRCh. 12.3 - Prob. 35CCRCh. 12.3 - Prob. 36CCRCh. 12.3 - Prob. 37CCRCh. 12.3 - Prob. 38CCRCh. 12.3 - Prob. 39CCRCh. 12.3 - Prob. 40CCRCh. 12.3 - Prob. 41CCRCh. 12.4 - Prob. 1GPCh. 12.4 - Prob. 2GPCh. 12.4 - Prob. 3GPCh. 12.4 - Prob. 4GPCh. 12.4 - Prob. 5GPCh. 12.4 - Prob. 6GPCh. 12.4 - Prob. 7IPCh. 12.4 - Prob. 8IPCh. 12.4 - Prob. 9IPCh. 12.4 - Prob. 10IPCh. 12.4 - Prob. 11IPCh. 12.4 - Prob. 12IPCh. 12.4 - Prob. 13IPCh. 12.4 - Prob. 14IPCh. 12.4 - Prob. 15IPCh. 12.4 - Prob. 16IPCh. 12.4 - Prob. 17IPCh. 12.4 - Prob. 18IPCh. 12.4 - Prob. 19IPCh. 12.4 - Prob. 20IPCh. 12.4 - Prob. 21IPCh. 12.4 - Prob. 22HPCh. 12.4 - Prob. 23HPCh. 12.4 - Prob. 24HPCh. 12.4 - Prob. 25HPCh. 12.4 - Prob. 26HPCh. 12.4 - Prob. 27HPCh. 12.4 - Prob. 28HPCh. 12.4 - Prob. 29STPCh. 12.4 - Prob. 30STPCh. 12.4 - Prob. 31STPCh. 12.4 - Prob. 32STPCh. 12.4 - Prob. 33CCRCh. 12.4 - Prob. 34CCRCh. 12.4 - Prob. 35CCRCh. 12.4 - Prob. 36CCRCh. 12.4 - Prob. 37CCRCh. 12.4 - Prob. 38CCRCh. 12.4 - Prob. 39CCRCh. 12.4 - Prob. 40CCRCh. 12.4 - Prob. 41CCRCh. 12.4 - Prob. 42CCRCh. 12.4 - Prob. 43CCRCh. 12.5 - Prob. 1GPCh. 12.5 - Prob. 2GPCh. 12.5 - Prob. 3GPCh. 12.5 - Prob. 4GPCh. 12.5 - Prob. 5GPCh. 12.5 - Prob. 6IPCh. 12.5 - Prob. 7IPCh. 12.5 - Prob. 8IPCh. 12.5 - Prob. 9IPCh. 12.5 - Prob. 10IPCh. 12.5 - Prob. 11IPCh. 12.5 - Prob. 12IPCh. 12.5 - Prob. 13IPCh. 12.5 - Prob. 14IPCh. 12.5 - Prob. 15IPCh. 12.5 - Prob. 16IPCh. 12.5 - Prob. 17IPCh. 12.5 - Prob. 18IPCh. 12.5 - Prob. 19IPCh. 12.5 - Prob. 20IPCh. 12.5 - Prob. 21IPCh. 12.5 - Prob. 22IPCh. 12.5 - Prob. 23IPCh. 12.5 - Prob. 24IPCh. 12.5 - Prob. 25IPCh. 12.5 - Prob. 26IPCh. 12.5 - Prob. 27IPCh. 12.5 - Prob. 28HPCh. 12.5 - Prob. 29HPCh. 12.5 - Prob. 30HPCh. 12.5 - Prob. 31HPCh. 12.5 - Prob. 32HPCh. 12.5 - Prob. 33HPCh. 12.5 - Prob. 34STPCh. 12.5 - Prob. 35STPCh. 12.5 - Prob. 36STPCh. 12.5 - Prob. 37STPCh. 12.5 - Prob. 38CCRCh. 12.5 - Prob. 39CCRCh. 12.5 - Prob. 40CCRCh. 12.5 - Prob. 41CCRCh. 12.5 - Prob. 42CCRCh. 12.5 - Prob. 43CCRCh. 12.5 - Prob. 44CCRCh. 12.5 - Prob. 45CCRCh. 12.5 - Prob. 46CCRCh. 12.5 - Prob. 47CCRCh. 12.5 - Prob. 48CCRCh. 12.5 - Prob. 49CCRCh. 12.5 - Prob. 50CCRCh. 12.5 - Prob. 51CCRCh. 12.6 - Prob. 1GPCh. 12.6 - Prob. 2GPCh. 12.6 - Prob. 3GPCh. 12.6 - Prob. 4GPCh. 12.6 - Prob. 5GPCh. 12.6 - Prob. 6IPCh. 12.6 - Prob. 7IPCh. 12.6 - Prob. 8IPCh. 12.6 - Prob. 9IPCh. 12.6 - Prob. 10IPCh. 12.6 - Prob. 11IPCh. 12.6 - Prob. 12IPCh. 12.6 - Prob. 13IPCh. 12.6 - Prob. 14IPCh. 12.6 - Prob. 15IPCh. 12.6 - Prob. 16IPCh. 12.6 - Prob. 17IPCh. 12.6 - Prob. 18IPCh. 12.6 - Prob. 19IPCh. 12.6 - Prob. 20IPCh. 12.6 - Prob. 21IPCh. 12.6 - Prob. 22IPCh. 12.6 - Prob. 23HPCh. 12.6 - Prob. 24HPCh. 12.6 - Prob. 25HPCh. 12.6 - Prob. 26HPCh. 12.6 - Prob. 27STPCh. 12.6 - Prob. 28STPCh. 12.6 - Prob. 29STPCh. 12.6 - Prob. 30STPCh. 12.6 - Prob. 31CCRCh. 12.6 - Prob. 32CCRCh. 12.6 - Prob. 33CCRCh. 12.6 - Prob. 34CCRCh. 12.6 - Prob. 35CCRCh. 12.6 - Prob. 36CCRCh. 12.6 - Prob. 37CCRCh. 12.6 - Prob. 38CCRCh. 12.6 - Prob. 39CCRCh. 12.6 - Prob. 40CCRCh. 12.6 - Prob. 41CCRCh. 12.6 - Prob. 42CCRCh. 12.6 - Prob. 43CCRCh. 12.6 - Prob. 44CCRCh. 12.6 - Prob. 45CCRCh. 12.6 - Prob. 46CCRCh. 12.6 - Prob. 47CCRCh. 12.7 - Prob. 1GPCh. 12.7 - Prob. 2GPCh. 12.7 - Prob. 3GPCh. 12.7 - Prob. 4GPCh. 12.7 - Prob. 5GPCh. 12.7 - Prob. 6IPCh. 12.7 - Prob. 7IPCh. 12.7 - Prob. 8IPCh. 12.7 - Prob. 9IPCh. 12.7 - Prob. 10IPCh. 12.7 - Prob. 11IPCh. 12.7 - Prob. 12IPCh. 12.7 - Prob. 13IPCh. 12.7 - Prob. 14IPCh. 12.7 - Prob. 15IPCh. 12.7 - Prob. 16IPCh. 12.7 - Prob. 17IPCh. 12.7 - Prob. 18IPCh. 12.7 - Prob. 19IPCh. 12.7 - Prob. 20IPCh. 12.7 - Prob. 21IPCh. 12.7 - Prob. 22IPCh. 12.7 - Prob. 23IPCh. 12.7 - Prob. 24IPCh. 12.7 - Prob. 25IPCh. 12.7 - Prob. 26HPCh. 12.7 - Prob. 27HPCh. 12.7 - Prob. 28HPCh. 12.7 - Prob. 29HPCh. 12.7 - Prob. 30HPCh. 12.7 - Prob. 31HPCh. 12.7 - Prob. 32STPCh. 12.7 - Prob. 33STPCh. 12.7 - Prob. 34STPCh. 12.7 - Prob. 35STPCh. 12.7 - Prob. 36CCRCh. 12.7 - Prob. 37CCRCh. 12.7 - Prob. 38CCRCh. 12.7 - Prob. 39CCRCh. 12.7 - Prob. 40CCRCh. 12.7 - Prob. 41CCRCh. 12.7 - Prob. 42CCRCh. 12.7 - Prob. 43CCRCh. 12.7 - Prob. 44CCRCh. 12.7 - Prob. 45CCRCh. 12.8 - Prob. 1GPCh. 12.8 - Prob. 2GPCh. 12.8 - Prob. 3GPCh. 12.8 - Prob. 4GPCh. 12.8 - Prob. 5IPCh. 12.8 - Prob. 6IPCh. 12.8 - Prob. 7IPCh. 12.8 - Prob. 8IPCh. 12.8 - Prob. 9IPCh. 12.8 - Prob. 10IPCh. 12.8 - Prob. 11IPCh. 12.8 - Prob. 12IPCh. 12.8 - Prob. 13IPCh. 12.8 - Prob. 14IPCh. 12.8 - Prob. 15IPCh. 12.8 - Prob. 16IPCh. 12.8 - Prob. 17IPCh. 12.8 - Prob. 18HPCh. 12.8 - Prob. 19HPCh. 12.8 - Prob. 20HPCh. 12.8 - Prob. 21HPCh. 12.8 - Prob. 22HPCh. 12.8 - Prob. 23STPCh. 12.8 - Prob. 24STPCh. 12.8 - Prob. 25STPCh. 12.8 - Prob. 26STPCh. 12.8 - Prob. 27CCRCh. 12.8 - Prob. 28CCRCh. 12.8 - Prob. 29CCRCh. 12.8 - Prob. 30CCRCh. 12.8 - Prob. 31CCRCh. 12.8 - Prob. 32CCRCh. 12.8 - Prob. 33CCRCh. 12.8 - Prob. 34CCRCh. 12.8 - Prob. 35CCRCh. 12.8 - Prob. 36CCRCh. 12.8 - Prob. 37CCRCh. 12.8 - Prob. 38CCRCh. 12.8 - Prob. 39CCRCh. 12.8 - Prob. 40CCRCh. 12.9 - Prob. 1GPCh. 12.9 - Prob. 2GPCh. 12.9 - Prob. 3GPCh. 12.9 - Prob. 4GPCh. 12.9 - Prob. 5IPCh. 12.9 - Prob. 6IPCh. 12.9 - Prob. 7IPCh. 12.9 - Prob. 8IPCh. 12.9 - Prob. 9IPCh. 12.9 - Prob. 10IPCh. 12.9 - Prob. 11IPCh. 12.9 - Prob. 12IPCh. 12.9 - Prob. 13IPCh. 12.9 - Prob. 14IPCh. 12.9 - Prob. 15IPCh. 12.9 - Prob. 16IPCh. 12.9 - Prob. 17IPCh. 12.9 - Prob. 18IPCh. 12.9 - Prob. 19HPCh. 12.9 - Prob. 20HPCh. 12.9 - Prob. 21HPCh. 12.9 - Prob. 22STPCh. 12.9 - Prob. 23STPCh. 12.9 - Prob. 24STPCh. 12.9 - Prob. 25STPCh. 12.9 - Prob. 26CCRCh. 12.9 - Prob. 27CCRCh. 12.9 - Prob. 28CCRCh. 12.9 - Prob. 29CCRCh. 12.9 - Prob. 30CCRCh. 12.9 - Prob. 31CCRCh. 12.9 - Prob. 32CCRCh. 12.9 - Prob. 33CCRCh. 12.9 - Prob. 34CCRCh. 12.9 - Prob. 35CCRCh. 12.9 - Prob. 36CCRCh. 12.9 - Prob. 37CCRCh. 12.9 - Prob. 38CCRCh. 12.9 - Prob. 39CCRCh. 12.9 - Prob. 40CCRCh. 12.9 - Prob. 41CCRCh. 12.9 - Prob. 42CCRCh. 12.9 - Prob. 43CCRCh. 12.9 - Prob. 44CCRCh. 12.10 - Prob. 1GPCh. 12.10 - Prob. 2GPCh. 12.10 - Prob. 3GPCh. 12.10 - Prob. 4GPCh. 12.10 - Prob. 5IPCh. 12.10 - Prob. 6IPCh. 12.10 - Prob. 7IPCh. 12.10 - Prob. 8IPCh. 12.10 - Prob. 9IPCh. 12.10 - Prob. 10IPCh. 12.10 - Prob. 11IPCh. 12.10 - Prob. 12IPCh. 12.10 - Prob. 13IPCh. 12.10 - Prob. 14IPCh. 12.10 - Prob. 15IPCh. 12.10 - Prob. 16IPCh. 12.10 - Prob. 17IPCh. 12.10 - Prob. 18IPCh. 12.10 - Prob. 19IPCh. 12.10 - Prob. 20IPCh. 12.10 - Prob. 21IPCh. 12.10 - Prob. 22IPCh. 12.10 - Prob. 23HPCh. 12.10 - Prob. 24HPCh. 12.10 - Prob. 25HPCh. 12.10 - Prob. 26HPCh. 12.10 - Prob. 27STPCh. 12.10 - Prob. 28STPCh. 12.10 - Prob. 29STPCh. 12.10 - Prob. 30STPCh. 12.10 - Prob. 31CCRCh. 12.10 - Prob. 32CCRCh. 12.10 - Prob. 33CCRCh. 12.10 - Prob. 34CCRCh. 12.10 - Prob. 35CCRCh. 12.10 - Prob. 36CCRCh. 12.10 - Prob. 37CCRCh. 12.10 - Prob. 38CCRCh. 12.10 - Prob. 39CCRCh. 12.10 - Prob. 40CCRCh. 12.10 - Prob. 41CCRCh. 12.10 - Prob. 42CCRCh. 12.10 - Prob. 43CCRCh. 12.10 - Prob. 44CCRCh. 12 - Prob. 1CRCh. 12 - Prob. 2CRCh. 12 - Prob. 3CRCh. 12 - Prob. 4CRCh. 12 - Prob. 5CRCh. 12 - Prob. 6CRCh. 12 - Prob. 7CRCh. 12 - Prob. 8CRCh. 12 - Prob. 9CRCh. 12 - Prob. 10CRCh. 12 - Prob. 11CRCh. 12 - Prob. 12CRCh. 12 - Prob. 13CRCh. 12 - Prob. 14CRCh. 12 - Prob. 15CRCh. 12 - Prob. 16CRCh. 12 - Prob. 17CRCh. 12 - Prob. 18CRCh. 12 - Prob. 19CRCh. 12 - Prob. 20CRCh. 12 - Prob. 21CRCh. 12 - Prob. 22CRCh. 12 - Prob. 23CRCh. 12 - Prob. 24CRCh. 12 - Prob. 25CRCh. 12 - Prob. 26CRCh. 12 - Prob. 27CRCh. 12 - Prob. 28CRCh. 12 - Prob. 29CRCh. 12 - Prob. 30CRCh. 12 - Prob. 31CRCh. 12 - Prob. 32CRCh. 12 - Prob. 33CRCh. 12 - 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