Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Hexagons

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , what is the length of diagonal ?

Possible Answers:

$11\sqrt3$

$44\sqrt3$

Correct answer:

Explanation:

When all the diagonals connecting opposite points of a regular hexagon are drawn in, congruent equilateral triangles are created. We can also see that the length of one such diagonal is merely twice the length of a side of the hexagon.

Use the perimeter to find the length of a side of the hexagon.

$\text{Length of Side}=\frac{\text{Perimeter}}{6}$

$\text{Length of Side}=\frac{66}{6}=11$

Double the length of a side to get the length of the wanted diagonal.

$\text{Length of Diagonal}=2(11)=22$

Report an Error

Example Question #1 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the hexagon above is , what is the length of diagonal ?

Possible Answers:

Correct answer:

Explanation:

Use the perimeter to find the length of a side of the hexagon.

$\text{Length of Side}=\frac{\text{Perimeter}}{6}$

$\text{Length of Side}=\frac{72}{6}=12$

Double the length of a side to get the length of the wanted diagonal.

$\text{Length of Diagonal}=2(12)=24$

Report an Error

Example Question #1 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , what is the length of diagonal ?

Possible Answers:

$12\sqrt3$

$14\sqrt3$

Correct answer:

Explanation:

Use the perimeter to find the length of a side of the hexagon.

$\text{Length of Side}=\frac{\text{Perimeter}}{6}$

$\text{Length of Side}=\frac{78}{6}=13$

Double the length of a side to get the length of the wanted diagonal.

$\text{Length of Diagonal}=2(13)=26$

Report an Error

Example Question #9 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , what is the length of diagonal ?

Possible Answers:

$20\sqrt3$

$15\sqrt3$

Correct answer:

Explanation:

Use the perimeter to find the length of a side of the hexagon.

$\text{Length of Side}=\frac{\text{Perimeter}}{6}$

$\text{Length of Side}=\frac{90}{6}=15$

Double the length of a side to get the length of the wanted diagonal.

$\text{Length of Diagonal}=2(15)=30$

Report an Error

Example Question #10 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , what is the length of diagonal ?

Possible Answers:

7.5

5.5

Correct answer:

Explanation:

Use the perimeter to find the length of a side of the hexagon.

$\text{Length of Side}=\frac{\text{Perimeter}}{6}$

$\text{Length of Side}=\frac{33}{6}=5.5$

Double the length of a side to get the length of the wanted diagonal.

$\text{Length of Diagonal}=2(5.5)=11$

Report an Error

Example Question #11 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , what is the length of diagonal ?

Possible Answers:

$9\sqrt3$

Correct answer:

Explanation:

Use the perimeter to find the length of a side of the hexagon.

$\text{Length of Side}=\frac{\text{Perimeter}}{6}$

$\text{Length of Side}=\frac{45}{6}=7.5$

Double the length of a side to get the length of the wanted diagonal.

$\text{Length of Diagonal}=2(7.5)=15$

Report an Error

Example Question #12 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is 105 , what is the length of diagonal ?

Possible Answers:

$30\sqrt3$

Correct answer:

Explanation:

Use the perimeter to find the length of a side of the hexagon.

$\text{Length of Side}=\frac{\text{Perimeter}}{6}$

$\text{Length of Side}=\frac{105}{6}=17.5$

Double the length of a side to get the length of the wanted diagonal.

$\text{Length of Diagonal}=2(17.5)=35$

Report an Error

Example Question #13 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is 231 , what is the length of diagonal ?

Possible Answers:

Correct answer:

Explanation:

Use the perimeter to find the length of a side of the hexagon.

$\text{Length of Side}=\frac{\text{Perimeter}}{6}$

$\text{Length of Side}=\frac{231}{6}=38.5$

Double the length of a side to get the length of the wanted diagonal.

$\text{Length of Diagonal}=2(38.5)=77$

Report an Error

Example Question #14 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon is , find the length of diagonal .

Possible Answers:

$\sqrt3$

The length of the diagonal cannot be determined.

$2\sqrt3$

Correct answer:

$2\sqrt3$

Explanation:

When the regular hexagon is divided into congruent equilateral triangles, it's easy to see that diagonal is comprised of two heights of two equilateral triangles. This holds true for the other diagonals when drawn in, as shown by dotted lines in the figure below:

Now, in order to find the length of the diagonal, we will need to first find the length of a side of the hexagon.

$\text{Length of Side}=\frac{\text{Perimeter}}{6}$

Plug in the given perimeter to find the length of a side for the given hexagon.

$\text{Length of Side}=\frac{12}{6}=2$

Notice that the height of the equilateral triangle creates two congruent 30-60-90 triangles whose side lengths are in the ratio of $1:\sqrt3:2$ .

Thus, we can set up the following proportion to find the length of the height:

$\frac{2}{2}=\frac{\text{height}}{\sqrt3}$

$\text{height}=\sqrt3$

Since the diagonal is made up of two of these heights, multiply by to find the length of the diagonal.

$\text{Length of Diagonal}=2\sqrt3$

Report an Error

Example Question #15 : How To Find The Length Of The Diagonal Of A Hexagon

If the perimeter of the regular hexagon above is , find the length of diagonal .

Possible Answers:

$7\sqrt3$

$\frac{3\sqrt3}{2}$

$14\sqrt3$

$\frac{5\sqrt3}{2}$

Correct answer:

$7\sqrt3$

Explanation:

Now, in order to find the length of the diagonal, we will need to first find the length of a side of the hexagon.

$\text{Length of Side}=\frac{\text{Perimeter}}{6}$

Plug in the given perimeter to find the length of a side for the given hexagon.

$\text{Length of Side}=\frac{42}{6}=7$

Notice that the height of the equilateral triangle creates two congruent 30-60-90 triangles whose side lengths are in the ratio of $1:\sqrt3:2$ .

Thus, we can set up the following proportion to find the length of the height:

$\frac{7}{2}=\frac{\text{height}}{\sqrt3}$

$\text{height}=\frac{7\sqrt3}{2}$

Since the diagonal is made up of two of these heights, multiply by to find the length of the diagonal.

$\text{Length of Diagonal}=2(\frac{7\sqrt3}{2})=7\sqrt3$

Report an Error

View Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

View Tutors

Jeffrey
Certified Tutor

View Tutors

Yongmao
Certified Tutor

Nankai University, Bachelor of Science, Chemistry. Washington University in St Louis, Doctor of Philosophy, Organic Chemistry.

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Seattle, Algebra Tutors in San Francisco-Bay Area, Math Tutors in Denver, French Tutors in New York City, English Tutors in Washington DC, GMAT Tutors in San Diego, French Tutors in Dallas Fort Worth, Spanish Tutors in San Diego, Algebra Tutors in Chicago, GMAT Tutors in San Francisco-Bay Area

Popular Courses & Classes

MCAT Courses & Classes in Denver, Spanish Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Los Angeles, GRE Courses & Classes in Atlanta, GRE Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Miami, LSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Washington DC, ACT Courses & Classes in Houston

Popular Test Prep

ISEE Test Prep in Boston, SAT Test Prep in San Diego, GMAT Test Prep in Los Angeles, ACT Test Prep in New York City, SAT Test Prep in Denver, GMAT Test Prep in Miami, SAT Test Prep in Miami, ACT Test Prep in Houston, ISEE Test Prep in Washington DC, SSAT Test Prep in San Francisco-Bay Area

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Intermediate Geometry : Hexagons

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Length Of The Diagonal Of A Hexagon

Example Question #1 : How To Find The Length Of The Diagonal Of A Hexagon

Example Question #1 : How To Find The Length Of The Diagonal Of A Hexagon

Example Question #9 : How To Find The Length Of The Diagonal Of A Hexagon

Example Question #10 : How To Find The Length Of The Diagonal Of A Hexagon

Example Question #11 : How To Find The Length Of The Diagonal Of A Hexagon

Example Question #12 : How To Find The Length Of The Diagonal Of A Hexagon

Example Question #13 : How To Find The Length Of The Diagonal Of A Hexagon

Example Question #14 : How To Find The Length Of The Diagonal Of A Hexagon

Example Question #15 : How To Find The Length Of The Diagonal Of A Hexagon

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: