Glencoe Math Accelerated, Student Edition
Glencoe Math Accelerated, Student Edition
1st Edition
ISBN: 9780076637980
Author: McGraw-Hill Glencoe
Publisher: MCG
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Chapter 12.4, Problem 21IP

(a)

To determine

To complete: The table.

(a)

Expert Solution
Check Mark

Answer to Problem 21IP

The complete table is given below.

Explanation of Solution

Given information:

Consider the given table.

    NameTriangular

    Pyramid

    		Square

    Pyramid

    		Pentagonal

    Pyramid

    Vertices45
    Faces6
    Edges8

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.

    NameTriangular PyramidSquare PyramidPentagonal Pyramid
    ShapeGlencoe Math Accelerated, Student Edition, Chapter 12.4, Problem 21IP , additional homework tip 1Glencoe Math Accelerated, Student Edition, Chapter 12.4, Problem 21IP , additional homework tip 2Glencoe Math Accelerated, Student Edition, Chapter 12.4, Problem 21IP , additional homework tip 3
    Vertices456
    Faces456
    Edges6810

Conclusion:

Therefore, the complete table is shown above.

(b)

To determine

To analyze: The relation between the vertices, faces, and edges.

(b)

Expert Solution
Check Mark

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.

    NameTriangular PyramidSquare PyramidPentagonal Pyramid
    ShapeGlencoe Math Accelerated, Student Edition, Chapter 12.4, Problem 21IP , additional homework tip 4Glencoe Math Accelerated, Student Edition, Chapter 12.4, Problem 21IP , additional homework tip 5Glencoe Math Accelerated, Student Edition, Chapter 12.4, Problem 21IP , additional homework tip 6
    Vertices456
    Faces456
    Edges6810

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
Check Mark

Answer to Problem 21IP

The required equation is V+F=E+2 .

Explanation of Solution

Given information:

Consider the given table.

    NameTriangular PyramidSquare PyramidPentagonal Pyramid
    ShapeGlencoe Math Accelerated, Student Edition, Chapter 12.4, Problem 21IP , additional homework tip 7Glencoe Math Accelerated, Student Edition, Chapter 12.4, Problem 21IP , additional homework tip 8Glencoe Math Accelerated, Student Edition, Chapter 12.4, Problem 21IP , additional homework tip 9
    Vertices456
    Faces456
    Edges6810

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 V , the number of faces is F and the number of edges is E . Write the an equation to show the relation between V , F and E .

  V+F=E+2

Conclusion:

Therefore, the required equation is V+F=E+2 .

Previous
Chapter 12.4, Problem 20IP
Next
Chapter 12.4, Problem 22HP

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 - Prob. 34CRCh. 12 - Prob. 35CRCh. 12 - Prob. 36CRCh. 12 - Prob. 37CRCh. 12 - Prob. 38CR

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