Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
bartleby

Videos

Expert Solution & Answer
Book Icon
Chapter 5.4, Problem 21PSC
Solution

a.

To find: The number of diagonals a triangle can have

A triangle has 0 diagonals.

Given:

A triangle.

Concept used:

Here, we are using the formula:

Diagonal of a polygon = n(n−3)2

(Where, “n” is side)

Calculation:

We know that,

A triangle has 3 sides.

So, diagonals of a triangle = n(n−3)2

(Where, “n” is side)

➜ 3(3−3)2

➜ 0

Conclusion: Hence, a triangle has 0 diagonals.

b.

To find: The number of diagonals a quadrilateral can have

A quadrilateral has 2 diagonals.

Given:

A quadrilateral.

Concept used:

Here, we are using the formula:

Diagonal of a polygon = n(n−3)2

(Where, “n” is side)

Calculation:

We know that,

A quadrilateral has 4 sides.

So, diagonals of a quadrilateral = n(n−3)2

(Where, “n” is side)

➜ 4(4−3)2

➜ 2

Conclusion: Hence, a quadrilateral has 2 diagonals.

c.

To find: The number of diagonals a five-sided polygon can have

A five-sided polygon have 5 diagonals.

Given:

Afive-sided polygon

Concept used:

Here, we are using the formula:

Diagonal of a polygon = n(n−3)2

(Where, “n” is side)

Calculation:

So, diagonals of a five-sided polygon = n(n−3)2

(Where, “n” is side)

➜ 5(5−3)2

➜ 5

Conclusion: Hence, a five-sided polygon have 5 diagonals.

d.

To find: The number of diagonals a six-sided polygon can have

A six-sided polygon have 9 diagonals.

Given:

A five-sided polygon

Concept used:

Here, we are using the formula:

Diagonal of a polygon = n(n−3)2

(Where, “n” is side)

Calculation:

So, diagonals of a six-sided polygon = n(n−3)2

(Where, “n” is side)

➜ 6(6−3)2

➜ 9

Conclusion: Hence, a six-sided polygon have 9 diagonals.

e.

To find: The number of diagonals meet at one vertex of a polygon with n sides.

The number of diagonals is n(n−3)

Given:

A polygon have n sides.

Concept used:

Here, we are using the formula:

Diagonal of a polygon = n(n−3)2

(Where, “n” is side)

Explanation:

We know that,

From each vertex we can draw n−3 diagonals.

So, the total number of diagonals is n(n−3)

Conclusion: Hence, the number of diagonals is n(n−3)

f.

To find: The number of vertices an n-sided polygon can have

The number of vertices is n

Given:

An n-sided polygon.

Explanation:

An n-sided polygon can have n vertices and from each vertex we can draw n−3 diagonals.

Conclusion: Hence, the number of vertices is n

g.

To find: The number of diagonals an n-sided polygon can have

The number of diagonals is n(n−3)

Given:

An n-sided polygon.

Explanation:

An n-sided polygon can have n vertices and from each vertex we can draw n−3 diagonals.

So, the total number of diagonals = n(n−3)

Conclusion: Hence, the number of diagonals is n(n−3)

Previous
Chapter 5.4, Problem 20PSB
Next
Chapter 5.4, Problem 22PSC

Chapter 5 Solutions

Geometry For Enjoyment And Challenge

Ch. 5.1 - Prob. 1PSACh. 5.1 - Prob. 2PSACh. 5.1 - Prob. 3PSACh. 5.1 - Prob. 4PSACh. 5.1 - Prob. 5PSACh. 5.1 - Prob. 6PSACh. 5.1 - Prob. 7PSACh. 5.1 - Prob. 8PSACh. 5.1 - Prob. 9PSACh. 5.1 - Prob. 10PSB
Ch. 5.1 - Prob. 11PSBCh. 5.1 - Prob. 12PSBCh. 5.1 - Prob. 13PSBCh. 5.1 - Prob. 14PSCCh. 5.1 - Prob. 15PSCCh. 5.2 - Prob. 1PSACh. 5.2 - Prob. 2PSACh. 5.2 - Prob. 3PSACh. 5.2 - Prob. 4PSACh. 5.2 - Prob. 5PSACh. 5.2 - Prob. 6PSACh. 5.2 - Prob. 7PSACh. 5.2 - Prob. 8PSACh. 5.2 - Prob. 9PSACh. 5.2 - Prob. 10PSACh. 5.2 - Prob. 11PSACh. 5.2 - Prob. 12PSACh. 5.2 - Prob. 13PSACh. 5.2 - Prob. 14PSACh. 5.2 - Prob. 15PSACh. 5.2 - Prob. 16PSACh. 5.2 - Prob. 17PSACh. 5.2 - Prob. 18PSACh. 5.2 - Prob. 19PSACh. 5.2 - Prob. 20PSACh. 5.2 - Prob. 21PSACh. 5.2 - Prob. 22PSBCh. 5.2 - Prob. 23PSBCh. 5.2 - Prob. 24PSBCh. 5.2 - Prob. 25PSCCh. 5.2 - Prob. 26PSCCh. 5.2 - Prob. 27PSCCh. 5.2 - Prob. 28PSCCh. 5.3 - Prob. 1PSACh. 5.3 - Prob. 2PSACh. 5.3 - Prob. 3PSACh. 5.3 - Prob. 4PSACh. 5.3 - Prob. 5PSACh. 5.3 - Prob. 6PSACh. 5.3 - Prob. 7PSACh. 5.3 - Prob. 8PSACh. 5.3 - Prob. 9PSACh. 5.3 - Prob. 10PSACh. 5.3 - Prob. 11PSACh. 5.3 - Prob. 12PSACh. 5.3 - Prob. 13PSACh. 5.3 - Prob. 14PSBCh. 5.3 - Prob. 15PSBCh. 5.3 - Prob. 16PSBCh. 5.3 - Prob. 17PSBCh. 5.3 - Prob. 18PSBCh. 5.3 - Prob. 19PSBCh. 5.3 - Prob. 20PSBCh. 5.3 - Prob. 21PSBCh. 5.3 - Prob. 22PSBCh. 5.3 - Prob. 23PSBCh. 5.3 - Prob. 24PSBCh. 5.3 - Prob. 25PSBCh. 5.3 - Prob. 26PSCCh. 5.3 - Prob. 27PSCCh. 5.3 - Prob. 28PSCCh. 5.3 - Prob. 29PSDCh. 5.3 - Prob. 30PSDCh. 5.4 - Prob. 1PSACh. 5.4 - Prob. 2PSACh. 5.4 - Prob. 3PSACh. 5.4 - Prob. 4PSACh. 5.4 - Prob. 5PSACh. 5.4 - Prob. 6PSACh. 5.4 - Prob. 7PSACh. 5.4 - Prob. 8PSACh. 5.4 - Prob. 9PSACh. 5.4 - Prob. 10PSACh. 5.4 - Prob. 11PSACh. 5.4 - Prob. 12PSACh. 5.4 - Prob. 13PSBCh. 5.4 - Prob. 14PSBCh. 5.4 - Prob. 15PSBCh. 5.4 - Prob. 16PSBCh. 5.4 - Prob. 17PSBCh. 5.4 - Prob. 18PSBCh. 5.4 - Prob. 19PSBCh. 5.4 - Prob. 20PSBCh. 5.4 - Prob. 21PSCCh. 5.4 - Prob. 22PSCCh. 5.5 - Prob. 1PSACh. 5.5 - Prob. 2PSACh. 5.5 - Prob. 3PSACh. 5.5 - Prob. 4PSACh. 5.5 - Prob. 5PSACh. 5.5 - Prob. 6PSACh. 5.5 - Prob. 7PSACh. 5.5 - Prob. 8PSACh. 5.5 - Prob. 9PSACh. 5.5 - Prob. 10PSACh. 5.5 - Prob. 11PSACh. 5.5 - Prob. 12PSACh. 5.5 - Prob. 13PSACh. 5.5 - Prob. 14PSACh. 5.5 - Prob. 15PSBCh. 5.5 - Prob. 16PSBCh. 5.5 - Prob. 17PSBCh. 5.5 - Prob. 18PSBCh. 5.5 - Prob. 19PSBCh. 5.5 - Prob. 20PSBCh. 5.5 - Prob. 21PSBCh. 5.5 - Prob. 22PSBCh. 5.5 - Prob. 23PSBCh. 5.5 - Prob. 24PSBCh. 5.5 - Prob. 25PSBCh. 5.5 - Prob. 26PSBCh. 5.5 - Prob. 27PSBCh. 5.5 - Prob. 28PSCCh. 5.5 - Prob. 29PSCCh. 5.5 - Prob. 30PSCCh. 5.6 - Prob. 1PSACh. 5.6 - Prob. 2PSACh. 5.6 - Prob. 3PSACh. 5.6 - Prob. 4PSACh. 5.6 - Prob. 5PSACh. 5.6 - Prob. 6PSACh. 5.6 - Prob. 7PSACh. 5.6 - Prob. 8PSACh. 5.6 - Prob. 9PSACh. 5.6 - Prob. 10PSACh. 5.6 - Prob. 11PSBCh. 5.6 - Prob. 12PSBCh. 5.6 - Prob. 13PSBCh. 5.6 - Prob. 14PSBCh. 5.6 - Prob. 15PSBCh. 5.6 - Prob. 16PSBCh. 5.6 - Prob. 17PSBCh. 5.6 - Prob. 18PSBCh. 5.6 - Prob. 19PSCCh. 5.6 - Prob. 20PSCCh. 5.6 - Prob. 21PSDCh. 5.7 - Prob. 1PSACh. 5.7 - Prob. 2PSACh. 5.7 - Prob. 3PSACh. 5.7 - Prob. 4PSACh. 5.7 - Prob. 5PSACh. 5.7 - Prob. 6PSACh. 5.7 - Prob. 7PSACh. 5.7 - Prob. 8PSACh. 5.7 - Prob. 9PSACh. 5.7 - Prob. 10PSACh. 5.7 - Prob. 11PSBCh. 5.7 - Prob. 12PSBCh. 5.7 - Prob. 13PSBCh. 5.7 - Prob. 14PSBCh. 5.7 - Prob. 15PSBCh. 5.7 - Prob. 16PSBCh. 5.7 - Prob. 17PSBCh. 5.7 - Prob. 18PSBCh. 5.7 - Prob. 19PSBCh. 5.7 - Prob. 20PSBCh. 5.7 - Prob. 21PSBCh. 5.7 - Prob. 22PSBCh. 5.7 - Prob. 23PSBCh. 5.7 - Prob. 24PSBCh. 5.7 - Prob. 25PSBCh. 5.7 - Prob. 26PSCCh. 5.7 - Prob. 27PSCCh. 5.7 - Prob. 28PSCCh. 5.7 - Prob. 29PSCCh. 5 - Prob. 1RPCh. 5 - Prob. 2RPCh. 5 - Prob. 3RPCh. 5 - Prob. 4RPCh. 5 - Prob. 5RPCh. 5 - Prob. 6RPCh. 5 - Prob. 7RPCh. 5 - Prob. 8RPCh. 5 - Prob. 9RPCh. 5 - Prob. 10RPCh. 5 - Prob. 11RPCh. 5 - Prob. 12RPCh. 5 - Prob. 13RPCh. 5 - Prob. 14RPCh. 5 - Prob. 15RPCh. 5 - Prob. 16RPCh. 5 - Prob. 17RPCh. 5 - Prob. 18RPCh. 5 - Prob. 19RPCh. 5 - Prob. 20RPCh. 5 - Prob. 21RPCh. 5 - Prob. 22RPCh. 5 - Prob. 23RPCh. 5 - Prob. 24RPCh. 5 - Prob. 25RPCh. 5 - Prob. 26RPCh. 5 - Prob. 27RPCh. 5 - Prob. 28RPCh. 5 - Prob. 29RPCh. 5 - Prob. 30RP

Additional Math Textbook Solutions

Find more solutions based on key concepts
Constructing and Graphing Discrete Probability Distributions In Exercises 19 and 20, (a) construct a probabilit...

Elementary Statistics: Picturing the World (7th Edition)

Find the additive inverse of each of the following integers. Write the answer in the simplest possible form. a....

A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)

In Exercises 55-62, find the derivative of y with respect to x, t, or θ, as appropriate. 55. y = ln (cos2 θ)

University Calculus: Early Transcendentals (4th Edition)

Find f( 3 ) if f( x )=4 x 2 +5x . (pp. 60-62)

Precalculus

30. Body Temperatures Based on the sample results in Data Set 3 “Body Temperatures” in Appendix B, assume that ...

Elementary Statistics (13th Edition)

A total of 28 percent of American males smoke cigarettes. 7 percent smoke cigars, and 5 percent smoke both ciga...

A First Course in Probability (10th Edition)

Knowledge Booster
Background pattern image
Geometry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Text book image
Elementary Geometry for College Students
Geometry
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Cengage Learning
SEE MORE TEXTBOOKS
An Introduction to Area | Teaching Maths | EasyTeaching; Author: EasyTeaching;https://www.youtube.com/watch?v=_uKKl8R1xBM;License: Standard YouTube License, CC-BY
Area of a Rectangle, Triangle, Circle & Sector, Trapezoid, Square, Parallelogram, Rhombus, Geometry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=JnLDmw3bbuw;License: Standard YouTube License, CC-BY