Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : How to find the length of the side of a hexagon

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 #891 : Plane Geometry

Find the length of a side of a regular hexagon that has its center at .

Possible Answers:

$30\sqrt3$

$24\sqrt3$

$16\sqrt3$

$8\sqrt3$

Correct answer:

$16\sqrt3$

Explanation:

This is a regular hexagon; therefore, when we draw in the diagonals, we will create identical equilateral triangles as shown by the figure:

Now, the given line segment also serves as the height to the newly created equilateral triangles. This height also splits an equilateral triangle into two congruent $30^\circ-60^\circ-90^\circ$ triangles.

Recall that $30^\circ-60^\circ-90^\circ$ triangles have side lengths that are in the ratio of $1:\sqrt3:2$ .

Substitute in the given height into the ratio in order to find the length of the base of the $30^\circ-60^\circ-90^\circ$ triangle.

$\frac{\text{height}}{\sqrt3}=\frac{\text{base}}{1}$

Substitute.

$\frac{24}{\sqrt3}=\frac{\text{base}}{1}$

Solve.

$\text{base}=\frac{24\sqrt3}{3}=8\sqrt3$

The length of the side of the hexagon is twice the length of the base.

$\text{side length}=2(\text{base})$

Substitute in the value of the length of the base to find the side length of the hexagon.

$\text{side length}=2(8\sqrt3)$

Solve.

$\text{side length}=16\sqrt3$

Report an Error

Example Question #81 : Hexagons

Find the length of a side of a regular hexagon that has its center at .

Possible Answers:

$\frac{26\sqrt3}{3}$

$18\sqrt3$

$\frac{55\sqrt3}{3}$

$\frac{52\sqrt3}{3}$

Correct answer:

$\frac{52\sqrt3}{3}$

Explanation:

This is a regular hexagon; therefore, when we draw in the diagonals, we will create identical equilateral triangles as shown by the figure:

Recall that $30^\circ-60^\circ-90^\circ$ triangles have side lengths that are in the ratio of $1:\sqrt3:2$ .

Substitute in the given height into the ratio in order to find the length of the base of the $30^\circ-60^\circ-90^\circ$ triangle.

$\frac{\text{height}}{\sqrt3}=\frac{\text{base}}{1}$

Substitute.

$\frac{26}{\sqrt3}=\frac{\text{base}}{1}$

Solve.

$\text{base}=\frac{26\sqrt3}{3}$

The length of the side of the hexagon is twice the length of the base.

$\text{side length}=2(\text{base})$

Substitute in the value of the length of the base to find the side length of the hexagon.

$\text{side length}=2\left(\frac{26\sqrt3}{3}\right)$

Solve.

$\text{side length}=\frac{52\sqrt3}{3}$

Report an Error

Example Question #82 : Hexagons

Find the length of a side of a regular hexagon that has its center at .

Possible Answers:

$19\sqrt3$

$30\sqrt3$

$20\sqrt3$

$10\sqrt3$

Correct answer:

$20\sqrt3$

Explanation:

This is a regular hexagon; therefore, when we draw in the diagonals, we will create identical equilateral triangles as shown by the figure:

Recall that $30^\circ-60^\circ-90^\circ$ triangles have side lengths that are in the ratio of $1:\sqrt3:2$ .

Substitute in the given height into the ratio in order to find the length of the base of the $30^\circ-60^\circ-90^\circ$ triangle.

$\frac{\text{height}}{\sqrt3}=\frac{\text{base}}{1}$

Substitute.

$\frac{30}{\sqrt3}=\frac{\text{base}}{1}$

Solve.

$\text{base}=\frac{30\sqrt3}{3}=10\sqrt3$

The length of the side of the hexagon is twice the length of the base.

$\text{side length}=2(\text{base})$

Substitute in the value of the length of the base to find the side length of the hexagon.

$\text{side length}=2(10\sqrt3)$

Solve.

$\text{side length}=20\sqrt3$

Report an Error

Example Question #83 : Hexagons

Find the length of a side of a regular hexagon that has its center at .

Possible Answers:

$\frac{32\sqrt3}{3}$

$\frac{128\sqrt3}{3}$

$\frac{64\sqrt3}{3}$

$\frac{125\sqrt3}{3}$

Correct answer:

$\frac{64\sqrt3}{3}$

Explanation:

This is a regular hexagon; therefore, when we draw in the diagonals, we will create identical equilateral triangles as shown by the figure:

Recall that $30^\circ-60^\circ-90^\circ$ triangles have side lengths that are in the ratio of $1:\sqrt3:2$ .

Substitute in the given height into the ratio in order to find the length of the base of the $30^\circ-60^\circ-90^\circ$ triangle.

$\frac{\text{height}}{\sqrt3}=\frac{\text{base}}{1}$

Substitute.

$\frac{32}{\sqrt3}=\frac{\text{base}}{1}$

Solve.

$\text{base}=\frac{32\sqrt3}{3}$

The length of the side of the hexagon is twice the length of the base.

$\text{side length}=2(\text{base})$

Substitute in the value of the length of the base to find the side length of the hexagon.

$\text{side length}=2\left(\frac{32\sqrt3}{3}\right)$

Solve.

$\text{side length}=\frac{64\sqrt3}{3}$

Report an Error

Example Question #84 : Hexagons

Find the length of a side of a regular hexagon that has its center at .

Possible Answers:

$5\sqrt3$

$4\sqrt3$

$\frac{14\sqrt3}{3}$

$\frac{10\sqrt3}{3}$

Correct answer:

$\frac{10\sqrt3}{3}$

Explanation:

This is a regular hexagon; therefore, when we draw in the diagonals, we will create identical equilateral triangles as shown by the figure:

Recall that $30^\circ-60^\circ-90^\circ$ triangles have side lengths that are in the ratio of $1:\sqrt3:2$ .

Substitute in the given height into the ratio in order to find the length of the base of the $30^\circ-60^\circ-90^\circ$ triangle.

$\frac{\text{height}}{\sqrt3}=\frac{\text{base}}{1}$

Substitute.

$\frac{5}{\sqrt3}=\frac{\text{base}}{1}$

Solve.

$\text{base}=\frac{5\sqrt3}{3}$

The length of the side of the hexagon is twice the length of the base.

$\text{side length}=2(\text{base})$

Substitute in the value of the length of the base to find the side length of the hexagon.

$\text{side length}=2\left(\frac{5\sqrt3}{3}\right)$

Solve.

$\text{side length}=\frac{10\sqrt3}{3}$

Report an Error

Example Question #85 : Hexagons

Find the length of a side of a regular hexagon that has its center at .

Possible Answers:

$\frac{16\sqrt3}{3}$

$\frac{10\sqrt3}{3}$

$4\sqrt3$

$\frac{19\sqrt3}{3}$

Correct answer:

$\frac{16\sqrt3}{3}$

Explanation:

This is a regular hexagon; therefore, when we draw in the diagonals, we will create identical equilateral triangles as shown by the figure:

Recall that $30^\circ-60^\circ-90^\circ$ triangles have side lengths that are in the ratio of $1:\sqrt3:2$ .

Substitute in the given height into the ratio in order to find the length of the base of the $30^\circ-60^\circ-90^\circ$ triangle.

$\frac{\text{height}}{\sqrt3}=\frac{\text{base}}{1}$

Substitute.

$\frac{8}{\sqrt3}=\frac{\text{base}}{1}$

Solve.

$\text{base}=\frac{8\sqrt3}{3}$

The length of the side of the hexagon is twice the length of the base.

$\text{side length}=2(\text{base})$

Substitute in the value of the length of the base to find the side length of the hexagon.

$\text{side length}=2\left(\frac{8\sqrt3}{3}\right)$

Solve.

$\text{side length}=\frac{16\sqrt3}{3}$

Report an Error

Example Question #86 : Hexagons

Find the length of a side of a regular hexagon that has its center at .

Possible Answers:

$\frac{7\sqrt3}{3}$

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

$\frac{4\sqrt3}{3}$

$\frac{5\sqrt3}{3}$

Correct answer:

$\frac{4\sqrt3}{3}$

Explanation:

This is a regular hexagon; therefore, when we draw in the diagonals, we will create identical equilateral triangles as shown by the figure:

Recall that $30^\circ-60^\circ-90^\circ$ triangles have side lengths that are in the ratio of $1:\sqrt3:2$ .

Substitute in the given height into the ratio in order to find the length of the base of the $30^\circ-60^\circ-90^\circ$ triangle.

$\frac{\text{height}}{\sqrt3}=\frac{\text{base}}{1}$

Substitute.

$\frac{2}{\sqrt3}=\frac{\text{base}}{1}$

Solve.

$\text{base}=\frac{2\sqrt3}{3}$

The length of the side of the hexagon is twice the length of the base.

$\text{side length}=2(\text{base})$

Substitute in the value of the length of the base to find the side length of the hexagon.

$\text{side length}=2\left(\frac{2\sqrt3}{3}\right)$

Solve.

$\text{side length}=\frac{4\sqrt3}{3}$

Report an Error

Example Question #18 : How To Find The Length Of The Side Of A Hexagon

Given: Regular Hexagon HEXAGO with center . Construct segments $\overline{CA}$ and $\overline{CO}$ to form Quadrilateral CAGO .

True or false: Quadrilateral CAGO is a rhombus.

Possible Answers:

False

True

Correct answer:

True

Explanation:

Below is regular Hexagon HEXAGO with center , a segment drawn from to each vertex - that is, each of its radii drawn.

Hexagon 2

Each angle of a regular hexagon measures $120^{\circ }$ ; by symmetry, each radius bisects an angle of the hexagon, so

$m \angle CAG = m \angle CGA = m\angle CGO = m \angle COG = 60 ^{\circ }$ .

Also, each central angle is one sixth of a complete circle, so $m \angle OCG = m \angle GCA = 60 ^{\circ }$ .

This makes $\bigtriangleup OCG$ and $\bigtriangleup GCA$ equilateral triangles. Therefore,

CO = OG = CG

and

CG = GA = AC

By transitivity,

CO = OG = GA = AC .

Quadrilateral CAGO has four sides of equal length and is consequently a rhombus.

Report an Error

Example Question #81 : Hexagons

Five sides of a hexagon are known to have length 10; the perimeter of the pentagon is 60.

True, false, or undetermined: The hexagon is regular.

Possible Answers:

True

False

Undetermined

Correct answer:

Undetermined

Explanation:

If the hexagon has perimeter 60, and five of its sides are known to have length 10, then the length of its sixth side is

60 - (10+ 10+ 10 + 10 + 10 ) = 60-50 = 10 .

All six sides are of the same length, so the hexagon is equilateral. However, for the hexagon to be regular, it must hold that all six angles are of the same measure as well - that is, it must also be equiangular. However, an equilateral hexagon may or may not be equiangular, as seen by the figures below; both are equilateral hexagons, but only the left one is equiangular.

Hexagons

Therefore, the question of whether the hexagon is regular cannot be answered without further information.

Report an Error

View Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

View Tutors

Momodou
Certified Tutor

Rochester Institute of Technology, Bachelor in Arts, Animation and Special Effects.

View Tutors

Anthony
Certified Tutor

CUNY New York City College of Technology, Bachelor of Science, Civil Engineering.

All Intermediate Geometry Resources

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

Popular Subjects

GRE Tutors in San Francisco-Bay Area, Spanish Tutors in Seattle, Physics Tutors in Seattle, GMAT Tutors in Washington DC, Spanish Tutors in San Diego, Math Tutors in San Diego, Chemistry Tutors in Phoenix, GRE Tutors in Los Angeles, Calculus Tutors in Miami, Spanish Tutors in Boston

Popular Courses & Classes

GRE Courses & Classes in Phoenix, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in San Diego, GRE Courses & Classes in Washington DC, SSAT Courses & Classes in Washington DC, SAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Denver, ISEE Courses & Classes in San Diego, Spanish Courses & Classes in Seattle, SSAT Courses & Classes in San Diego

Popular Test Prep

GRE Test Prep in Washington DC, GMAT Test Prep in Phoenix, GMAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Seattle, SAT Test Prep in New York City, ACT Test Prep in Miami, MCAT Test Prep in Los Angeles, SSAT Test Prep in Washington DC, GRE Test Prep in Philadelphia, SSAT Test Prep in Denver

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 : How to find the length of the side of a hexagon

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #891 : Plane Geometry

Example Question #81 : Hexagons

Example Question #82 : Hexagons

Example Question #83 : Hexagons

Example Question #84 : Hexagons

Example Question #85 : Hexagons

Example Question #86 : Hexagons

Example Question #18 : How To Find The Length Of The Side Of A Hexagon

Example Question #81 : Hexagons

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: