GMAT Math : Polygons

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Calculating The Length Of A Side Of A Polygon

The perimeter of a regular pentagon is three kilometers. Give its sidelength in meters.

Possible Answers:

$50 \textrm{ m}$

$500 \textrm{ m}$

$60 \textrm{ m}$

$600 \textrm{ m}$

$375 \textrm{ m}$

Correct answer:

$600 \textrm{ m}$

Explanation:

One kilometer is equal to 1,000 meters, so two kilometers comprise 3,000 meters. A regular pentagon has five sides of equal length, so divide by 5 to get the sidelength: $3,000 \div 5 = 600$ meters.

Report an Error

Example Question #5 : Calculating The Length Of A Side Of A Polygon

Six regular polygons each have perimeter one mile. The polygons are an equilateral triangle, a square, a pentagon, a hexagon, an octagon, and a decagon (ten-sided polygon). What is the mean of their sidelengths?

Possible Answers:

$1,240 \textrm{ ft}$

$1,320\textrm{ ft}$

$1,056 \textrm{ ft }$

$1,034\textrm{ ft}$

$880\textrm{ ft}$

Correct answer:

$1,034\textrm{ ft}$

Explanation:

The sidelength of a regular polygon is the perimeter of one mile, or 5,280 feet, divided by the number of sides. Therefore, the sidelengths of the six shapes are:

Triangle: $5,280 \div 3 = 1,760 \textrm{ ft}$

Square: $5,280 \div 4 = 1,320 \textrm{ ft}$

Pentagon: $5,280 \div 5 = 1,056 \textrm{ ft}$

Hexagon: $5,280 \div 6 = 880 \textrm{ ft}$

Octagon: $5,280 \div 8 = 660 \textrm{ ft}$

Decagon: $5,280 \div 10 = 528 \textrm{ ft}$

The mean of the six sidelengths:

$(1,760+1,320+1,056+880+660+528 ) \div 6 = 1,034$ feet

Report an Error

Example Question #6 : Calculating The Length Of A Side Of A Polygon

If the shape $\textup{ABCDEF}$ is a regular hexagon with side length of 2x+6 and a perimeter of meters, what is the length of one side?

Possible Answers:

$3\ \textup{meters}$

$15\ \textup{meters}$

$5\ \textup{meters}$

$9\ \textup{meters}$

$12\ \textup{meters}$

Correct answer:

$12\ \textup{meters}$

Explanation:

Perimeter is the total distance around a shape. Here we have a regular (all sides are equal) hexagon with side distance 2x+6. Multiplying this expression by 6 gives us our perimeter.

$\small 72=6*(2x+6)=12x+36$

$\small 72-36=12x$

$\small 12x=36$

$\small x=3$

But we are not done yet. We need to plug this back in to get the side length

$\small 2(3)+6=9+6=15$

so 15 meters

Alternatively, we could divide 72 by 6 to get 12 meters.

Report an Error

Example Question #3 : Calculating The Length Of A Side Of A Polygon

A regular hexagon has perimeter $2^{N}$ . Which of the following is equal to the length of one side?

Possible Answers:

$\frac{2^{N-1} }{ 3}$

$3^{-N}$

$2^{N - 6}$

$3 \cdot 2 ^{N-2}$

$2^{\frac{N}{6}}$

Correct answer:

$\frac{2^{N-1} }{ 3}$

Explanation:

A hexagon has six sides of equal length, so divide the perimeter by 6, which is the product of 2 and 3:

$\frac{2^{N}}{6} = \frac{2^{N}}{2 \cdot 3} = \frac{2^{N}}{2^{1} \cdot 3} = \frac{2^{N-1} }{ 3}$

Report an Error

Example Question #3 : Calculating The Length Of A Side Of A Polygon

A regular octagon has perimeter $2^{N}$ . Give the length of one of its sides.

Possible Answers:

$2^{ \frac{1}{3}N}$

$2^{N -3}$

$2^{N -2}$

$2^{N -1}$

$2^{ \frac{1}{2}N}$

Correct answer:

$2^{N -3}$

Explanation:

A regular octagon has eight sides of equal length, so divide the perimeter by 8, or equivalently, $2^{3}$ :

$\frac{2^{N}}{2^{3}} = 2^{N-3}$ .

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GRE Tutors in Washington DC, English Tutors in Los Angeles, Biology Tutors in Atlanta, Computer Science Tutors in Seattle, Algebra Tutors in Seattle, English Tutors in Washington DC, Physics Tutors in Atlanta, Computer Science Tutors in San Diego, Spanish Tutors in Atlanta, Biology Tutors in Philadelphia

Popular Courses & Classes

GMAT Courses & Classes in Denver, Spanish Courses & Classes in Los Angeles, SSAT Courses & Classes in Seattle, ACT Courses & Classes in Denver, GRE Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Seattle, SAT Courses & Classes in Los Angeles, ACT Courses & Classes in Houston, SAT Courses & Classes in Houston, MCAT Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Atlanta, GMAT Test Prep in Seattle, MCAT Test Prep in Washington DC, MCAT Test Prep in Houston, GMAT Test Prep in Houston, LSAT Test Prep in Miami, LSAT Test Prep in Denver, ACT Test Prep in Houston, LSAT Test Prep in Los Angeles

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)

Email address:
Your name:
Feedback:

GMAT Math : Polygons

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2 : Calculating The Length Of A Side Of A Polygon

Example Question #5 : Calculating The Length Of A Side Of A Polygon

Example Question #6 : Calculating The Length Of A Side Of A Polygon

Example Question #3 : Calculating The Length Of A Side Of A Polygon

Example Question #3 : Calculating The Length Of A Side Of A Polygon

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details