Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : How to find the area of a pentagon

Study concepts, example questions & explanations for SSAT Upper Level Math

Create An Account

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Area Of A Pentagon

Find the exact area of a pentagon if the side length is .

Possible Answers:

$9\sqrt{25+10\sqrt5}$

$6\sqrt{35\sqrt5}$

$\sqrt{25+10\sqrt5}$

$15+90\sqrt5$

$9\sqrt{10\sqrt5}$

Correct answer:

$9\sqrt{25+10\sqrt5}$

Explanation:

Write the formula for the area of a pentagon.

$A=\frac{s^{2}}{4}\sqrt{5(5+2\sqrt5)}$

Substitute the side length and simplify.

$A=\frac{6^{2}}{4}\sqrt{5(5+2\sqrt5)}$

$A= 9\sqrt{25+10\sqrt5}$

Report an Error

Example Question #2 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon that has a side length of and an apothem of .

Possible Answers:

30x^2

120x^2

30x

60x^2

Correct answer:

30x^2

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

To find the perimeter of the pentagon,

$\text{Perimeter}=5(side)$

For the given pentagon,

$\text{Perimeter}=5\times 6x=30x$

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(30x)(2x)=30x^2$

Report an Error

Example Question #3 : How To Find The Area Of A Pentagon

Find the area of a regular pentagon that has a side length of and an apothem of .

Possible Answers:

2000

500

750

1500

Correct answer:

750

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

To find the perimeter of the pentagon,

$\text{Perimeter}=5(side)$

For the given pentagon,

$\text{Perimeter}=5\times20=100$

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(100)(15)=750$

Report an Error

Example Question #1 : How To Find The Area Of A Pentagon

Find the area of a regular pentagon with a side length of .

Possible Answers:

27.53

98.21

29.11

41.21

Correct answer:

27.53

Explanation:

Use the following formula to find the area of a regular pentagon:

$\text{Area}=\frac{1}{4}\sqrt{5(5+2\sqrt5)}(side)^2$

Plugging in the information given by the question,

$\text{Area}=\frac{1}{4}\sqrt{5(5+2\sqrt5)}(4)^2=27.53$

Report an Error

Example Question #5 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon with side lengths of and an apothem of .

Possible Answers:

50z

75z^2

75z

150z

Correct answer:

75z

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

To find the perimeter of the pentagon,

$\text{Perimeter}=5(side)$

For the given pentagon,

$\text{Perimeter}=5\times 5z =25z$

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(25z)(6)=75z$

Report an Error

Example Question #6 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon that has a side length of and an apothem of .

Possible Answers:

160a^2

120a^2

80a

80a^2

Correct answer:

80a^2

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

To find the perimeter of the pentagon,

$\text{Perimeter}=5(side)$

For the given pentagon,

$\text{Perimeter}=5\times 8a=40a$

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(40a)(4a)=80a^2$

Report an Error

Example Question #7 : How To Find The Area Of A Pentagon

In terms of , find the area of a regular pentagon with side lengths of 12b and an apothem of 10b .

Possible Answers:

400b^2

200b^2

300b^2

600b^2

Correct answer:

300b^2

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

To find the perimeter of the pentagon,

$\text{Perimeter}=5(side)$

For the given pentagon,

$\text{Perimeter}=5\times 12b=60b$

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(60b)(10b)=300b^2$

Report an Error

Example Question #8 : How To Find The Area Of A Pentagon

The area of a regular polygon is 512 . If the length of its apothem is , what is the length of each side of the pentagon?

Possible Answers:

20.8

22.2

18.2

25.6

Correct answer:

25.6

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

For the given pentagon,

$512=\frac{1}{2}(Perimeter)(8)$

8(Perimeter)=1024

Perimeter=128

To find the length of each side of the pentagon, divide the perimeter by .

Side=25.6

Report an Error

Example Question #1 : How To Find The Area Of A Pentagon

A regular pentagon has an area of 250 . Find the length of each side of the pentagon if the apothem has a length of .

Possible Answers:

Correct answer:

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

For the given pentagon,

$250=\frac{1}{2}(Perimeter)(5)$

5(Perimeter)=500

Perimeter=100

To find the length of each side of the pentagon, divide the perimeter by .

Side=20

Report an Error

Example Question #10 : How To Find The Area Of A Pentagon

The area of a regular pentagon is 410 . Find the length of a side of the pentagon if the apothem has a length of .

Possible Answers:

$\frac{41}{3}$

$\frac{15}{2}$

$\frac{61}{3}$

Correct answer:

$\frac{41}{3}$

Explanation:

To find the area of a regular polygon,

$\text{Area}=\frac{1}{2}(Perimeter)(apothem)$

For the given pentagon,

$410=\frac{1}{2}(Perimeter)(12)$

12(Perimeter)=820

$Perimeter=\frac{820}{12}$

To find the length of each side of the pentagon, divide the perimeter by .

$Side=\frac{820}{60}=\frac{41}{3}$

Report an Error

View SSAT- Upper Level Tutors

Joseph
Certified Tutor

Bank Street College of Education , Master's/Graduate, Early Childhood and Childhood General Education.

View SSAT- Upper Level Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View SSAT- Upper Level Tutors

Shivansh
Certified Tutor

University of British Columbia, Bachelor, Math major and data science minor .

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in Miami, Statistics Tutors in Chicago, Reading Tutors in Atlanta, Computer Science Tutors in Dallas Fort Worth, Chemistry Tutors in Boston, SAT Tutors in Atlanta, LSAT Tutors in Philadelphia, English Tutors in San Francisco-Bay Area, MCAT Tutors in San Diego, MCAT Tutors in New York City

Popular Courses & Classes

Spanish Courses & Classes in Atlanta, Spanish Courses & Classes in Houston, GRE Courses & Classes in Atlanta, SSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Philadelphia, GRE Courses & Classes in Boston, Spanish Courses & Classes in Washington DC, GMAT Courses & Classes in Phoenix, LSAT Courses & Classes in Miami

Popular Test Prep

SSAT Test Prep in Atlanta, LSAT Test Prep in Atlanta, LSAT Test Prep in Philadelphia, GMAT Test Prep in Phoenix, GMAT Test Prep in Boston, GRE Test Prep in Miami, GRE Test Prep in Atlanta, GRE Test Prep in Boston, MCAT Test Prep in Denver, MCAT Test Prep in Boston

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

SSAT Upper Level Math : How to find the area of a pentagon

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Area Of A Pentagon

Example Question #2 : How To Find The Area Of A Pentagon

Example Question #3 : How To Find The Area Of A Pentagon

Example Question #1 : How To Find The Area Of A Pentagon

Example Question #5 : How To Find The Area Of A Pentagon

Example Question #6 : How To Find The Area Of A Pentagon

Example Question #7 : How To Find The Area Of A Pentagon

Example Question #8 : How To Find The Area Of A Pentagon

Example Question #1 : How To Find The Area Of A Pentagon

Example Question #10 : How To Find The Area Of A Pentagon

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: