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

← Previous 1 2 3 4 5 6 7 8 9 … 15 16 Next →

Example Question #41 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

Possible Answers:

$150\sqrt3$

$120\sqrt3$

$90\sqrt3$

$180\sqrt3$

Correct answer:

$120\sqrt3$

Explanation:

When all the diagonals of the regular hexagon are drawn in, you should notice that six congruent equilateral triangles are created.

Thus, we know that the given line segment, also known as an apothem, acts as the height of an equilateral triangle. The apothem also creates two congruent 30-60-90 triangles.

Thus, we can use the ratio of the side lengths to find the length of the base of one of the 30-60-90 triangles.

Recall that the ratios of the side lengths in a 30-60-90 triangle are $1:\sqrt3:2$ .

We can then set up the following equation:

$\frac{14}{\sqrt3}=\frac{\text{base}}{1}$

The length of the base is then $\frac{30}{\sqrt3}=10\sqrt3$ .

Now, the length of this base is half the length of a side of the hexagon. Multiply the base by two to find the length of a side:

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

$\text{side}=2(10\sqrt3)=20\sqrt3$

Next, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Plug in the side length to find the perimeter:

$\text{Perimeter}=6(20\sqrt3)=120\sqrt3$

Report an Error

Example Question #42 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

Possible Answers:

$12\sqrt3$

$8\sqrt3$

$10\sqrt3$

$14\sqrt3$

Correct answer:

$8\sqrt3$

Explanation:

When all the diagonals of the regular hexagon are drawn in, you should notice that six congruent equilateral triangles are created.

Thus, we know that the given line segment, also known as an apothem, acts as the height of an equilateral triangle. The apothem also creates two congruent 30-60-90 triangles.

Thus, we can use the ratio of the side lengths to find the length of the base of one of the 30-60-90 triangles.

Recall that the ratios of the side lengths in a 30-60-90 triangle are $1:\sqrt3:2$ .

We can then set up the following equation:

$\frac{14}{\sqrt3}=\frac{\text{base}}{1}$

The length of the base is then $\frac{2}{\sqrt3}=\frac{2\sqrt3}{3}$ .

Now, the length of this base is half the length of a side of the hexagon. Multiply the base by two to find the length of a side:

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

$\text{side}=2(\frac{2\sqrt3}{3})=\frac{4\sqrt3}{3}$

Next, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Plug in the side length to find the perimeter:

$\text{Perimeter}=6(\frac{4\sqrt3}{3})=8\sqrt3$

Report an Error

Example Question #43 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

Possible Answers:

$109\sqrt3$

$108\sqrt3$

$100\sqrt3$

$116\sqrt3$

Correct answer:

$108\sqrt3$

Explanation:

When all the diagonals of the regular hexagon are drawn in, you should notice that six congruent equilateral triangles are created.

Thus, we know that the given line segment, also known as an apothem, acts as the height of an equilateral triangle. The apothem also creates two congruent 30-60-90 triangles.

Thus, we can use the ratio of the side lengths to find the length of the base of one of the 30-60-90 triangles.

Recall that the ratios of the side lengths in a 30-60-90 triangle are $1:\sqrt3:2$ .

We can then set up the following equation:

$\frac{14}{\sqrt3}=\frac{\text{base}}{1}$

The length of the base is then $\frac{27}{\sqrt3}=9\sqrt3$ .

Now, the length of this base is half the length of a side of the hexagon. Multiply the base by two to find the length of a side:

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

$\text{side}=2(9\sqrt3)=18\sqrt3$

Next, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Plug in the side length to find the perimeter:

$\text{Perimeter}=6(18\sqrt3)=108\sqrt3$

Report an Error

Example Question #44 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

Possible Answers:

$96\sqrt3$

$160\sqrt3$

$128\sqrt3$

$136\sqrt3$

Correct answer:

$128\sqrt3$

Explanation:

When all the diagonals of the regular hexagon are drawn in, you should notice that six congruent equilateral triangles are created.

Thus, we know that the given line segment, also known as an apothem, acts as the height of an equilateral triangle. The apothem also creates two congruent 30-60-90 triangles.

Thus, we can use the ratio of the side lengths to find the length of the base of one of the 30-60-90 triangles.

Recall that the ratios of the side lengths in a 30-60-90 triangle are $1:\sqrt3:2$ .

We can then set up the following equation:

$\frac{14}{\sqrt3}=\frac{\text{base}}{1}$

The length of the base is then $\frac{32}{\sqrt3}=\frac{32\sqrt3}{3}$ .

Now, the length of this base is half the length of a side of the hexagon. Multiply the base by two to find the length of a side:

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

$\text{side}=2(\frac{32\sqrt3}{3})=\frac{64\sqrt3}{3}$

Next, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Plug in the side length to find the perimeter:

$\text{Perimeter}=6(\frac{64\sqrt3}{3})=128\sqrt3$

Report an Error

Example Question #45 : How To Find The Perimeter Of A Hexagon

Find the perimeter of the regular hexagon below:

Possible Answers:

$205\sqrt3$

$220\sqrt3$

$135\sqrt3$

$180\sqrt3$

Correct answer:

$180\sqrt3$

Explanation:

When all the diagonals of the regular hexagon are drawn in, you should notice that six congruent equilateral triangles are created.

Thus, we know that the given line segment, also known as an apothem, acts as the height of an equilateral triangle. The apothem also creates two congruent 30-60-90 triangles.

Thus, we can use the ratio of the side lengths to find the length of the base of one of the 30-60-90 triangles.

Recall that the ratios of the side lengths in a 30-60-90 triangle are $1:\sqrt3:2$ .

We can then set up the following equation:

$\frac{14}{\sqrt3}=\frac{\text{base}}{1}$

The length of the base is then $\frac{45}{\sqrt3}=15\sqrt3$ .

Now, the length of this base is half the length of a side of the hexagon. Multiply the base by two to find the length of a side:

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

$\text{side}=2(15\sqrt3)=30\sqrt3$

Next, recall how to find the perimeter of a regular hexagon:

$\text{Perimeter}=6(\text{side})$

Plug in the side length to find the perimeter:

$\text{Perimeter}=6(30\sqrt3)=180\sqrt3$

Report an Error

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

A regular hexagon has an apothem of length $7\sqrt{3}$ . Find the area of the circle that encompasses that hexagon:

Possible Answers:

$212\pi$ cm^2

None of the other answers

$108\pi$ cm^2

$144\pi$ cm^2

$196\pi$ cm^2

Correct answer:

$196\pi$ cm^2

Explanation:

When we segment the hexagon into smaller triangles we come out with a nice looking right triangle.

We know our apothem is $7\sqrt{3}$ cm, so that leaves us with a base of 7cm and a hypotenuse of 14 cm.

Looking at the picture, we can see that the hypotenuse of this triangle is also the radius of the outlying circle:

With our radius of 14 cm, we can plug into $Area =\pi r^2$ for circles and come up with an answer of $196\pi$ cm^2

Report an Error

Example Question #2 : How To Find The Length Of The Diagonal Of A Hexagon

Suppose the length of the hexagon has a side length of a+b . What is the diagonal of the hexagon?

Possible Answers:

6a+6b

2a+2b

3a+3b

$\frac{1}{6}a+\frac{1}{6}b$

a+b

Correct answer:

2a+2b

Explanation:

The hexagon is composed of 6 combined equilateral triangles, with 1 vertex from each equilateral joining the center point.

Therefore, since the side length of the hexagon is a+b , and each side length of the equilateral triangle is equal, then all side lengths of the equilateral triangles must be a+b .

Two side lengths of the equilateral triangle joins to create the diagonal of the hexagon.

2(a+b)=2a+2b

The diagonal length is 2a+2b .

Report an Error

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

Suppose a length of a hexagon is . What must be the diagonal length of the hexagon?

Possible Answers:

Correct answer:

Explanation:

The hexagon can be broken down into 6 equilateral triangles. Each side of the equilateral triangle is equal. Two of the combined lengths of the equilateral triangles join to form the diagonal of the hexagon.

Therefore, the diagonal is twice the side length of the hexagon.

$20\cdot 2=40$

Report an Error

Example Question #4 : 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:

$7\sqrt3$

$\frac{7\sqrt3}{2}$

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.

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

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

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

$\text{Length of Diagonal}=2(7)=14$

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:

$10\sqrt3$

$20\sqrt3$

Correct answer:

Explanation:

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

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

$\text{Length of Side}=\frac{60}{6}=10$

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

$\text{Length of Diagonal}=2(10)=20$

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 … 15 16 Next →

View Tutors

Shirin
Certified Tutor

University of New Brunswick, Bachelor of Science, Chemical Engineering.

View Tutors

Amit Kumar
Certified Tutor

sanjay gandhi postgraduate medical science , Doctorate (PhD), Genetics molecular biology .

View Tutors

Priyanvada
Certified Tutor

University of North Texas, Doctor of Philosophy, Materials Engineering.

All Intermediate Geometry Resources

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

Popular Subjects

Calculus Tutors in Dallas Fort Worth, Spanish Tutors in Washington DC, Algebra Tutors in New York City, GRE Tutors in Miami, Statistics Tutors in Denver, Algebra Tutors in San Diego, LSAT Tutors in Denver, Reading Tutors in Atlanta, Algebra Tutors in Houston, GMAT Tutors in Los Angeles

Popular Courses & Classes

Spanish Courses & Classes in Denver, GMAT Courses & Classes in New York City, GRE Courses & Classes in Atlanta, GRE Courses & Classes in Boston, ISEE Courses & Classes in Phoenix, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Chicago, SAT Courses & Classes in San Diego, SSAT Courses & Classes in Miami, SAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

SAT Test Prep in Los Angeles, ACT Test Prep in San Diego, MCAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Seattle, MCAT Test Prep in Philadelphia, ISEE Test Prep in Phoenix, ISEE Test Prep in Philadelphia, MCAT Test Prep in Chicago, SSAT Test Prep in Miami, LSAT 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 : Hexagons

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #41 : How To Find The Perimeter Of A Hexagon

Example Question #42 : How To Find The Perimeter Of A Hexagon

Example Question #43 : How To Find The Perimeter Of A Hexagon

Example Question #44 : How To Find The Perimeter Of A Hexagon

Example Question #45 : How To Find The Perimeter Of A Hexagon

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

Example Question #2 : 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 #4 : 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

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: