Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : Area of Polygons

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

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

Example Question #982 : Ssat Upper Level Quantitative (Math)

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

Possible Answers:

120

180

Correct answer:

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,

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

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(60)(3)=90$

Report an Error

Example Question #983 : Ssat Upper Level Quantitative (Math)

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

Possible Answers:

Correct answer:

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,

$\text{Perimeter}=5\times6=30$

So then, to find the area of the pentagon,

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

Report an Error

Example Question #11 : How To Find The Area Of A Pentagon

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

Possible Answers:

180

120

240

Correct answer:

120

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,

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

So then, to find the area of the pentagon,

$\text{Area}=\frac{1}{2}(60)(4)=120$

Report an Error

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

The volume of a cube is 1,000 cubic centimeters. Using the conversion factor 2.5 centimeters = 1 inch, give its surface area in square inches, rounding to the nearest square inch.

Possible Answers:

96 square inches

75 square inches

108 square inches

100 square inches

144 square inches

Correct answer:

96 square inches

Explanation:

The surface area of a cube is six times the square of its sidelength, so we find the sidelength. This is the cube root of volume 1,000, so

$\sqrt[3]{1000}$ =10 centimeters.

To rewrite this as inches, divide by 2.5:

$\div$ 2.5 = 4 inches

The surface area of the cube in square inches is

$6\times$ $4^{2}$ = 96 square inches.

Report an Error

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

The volume of a cube is 64 cubic inches. Find the side length of the cube and its surface area.

Possible Answers:

$4\ in,64\ in^{2}$

$8\ in,96\ in^{2}$

$4\ in,16\ in^{2}$

$4\ in,96\ in^{2}$

$8\ in,64\ in^{2}$

Correct answer:

$4\ in,96\ in^{2}$

Explanation:

The volume of a cube is s^3 where is the length of one edge, so is the cube root of volume:

$Volume=64\Rightarrow s=\sqrt[3]{64}=4\ in$

A cube has six faces and the surface area of a cube is 6s^2 . So we can write:

Surface area = $6s^2=6\times 4^2=6\times 16=96\ in^{2}$

Report an Error

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

A square has an area of 16 square inches. Give the diagonal of the square.

Possible Answers:

$4\sqrt{2}$

$4\sqrt{3}$

$2\sqrt{2}$

Correct answer:

$4\sqrt{2}$

Explanation:

In order to determine the length of the diagonal of a square we would use the Pythagorean Theorem. First we should find the side length:

$Side=\sqrt{area}=\sqrt{16}=4\ inches$

Now, "square" the length of one side and multiply by 2, then take the square root of that number to get the length of the diagonal:

$Diagonal=\sqrt{4^2\times 2}=4\sqrt{2}\ inches$

Report an Error

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

John is going to apply a fertilizer to his farm which has a dimension of 200 feet by 200 feet. Every pound of the fertilizer that he is going to use is sufficient for 40 square feet. If the fertilizer costs 2 dollars per pound, how much he should spend to fertilize his farm?

Possible Answers:

$\$2500$

$\$1000$

$\$1500$

$\$2000$

$\$4000$

Correct answer:

$\$2000$

Explanation:

The area of the farm is:

$A=200\times 200=40000$ square feet. So the amount of the fertilizer he needs can be calculated as:

$40000\div 40=1000$ pounds

Every pound of the fertilizer costs $2, so he needs to spend $2\times 1000=2000$ dollars.

Report an Error

Example Question #4 : How To Find The Area Of A Square

The diagonal length of a square is . Find the area of the square in terms of .

Possible Answers:

2t^2

$t\sqrt{2}$

$\frac{t^2}{2}$

$\frac{t\sqrt{2}}2{}$

$\frac{t\sqrt{2}}{4}$

Correct answer:

$\frac{t^2}{2}$

Explanation:

We need to use the Pythagorean Theorem in order to solve this problem. We can write:

d^2=s^2+s^2=2s^2

where is the diagonal length and is the side length. The diagonal length of the square is d=t , so we can write:

$t^2=2s^2\Rightarrow s^2=\frac{t^2}{2}\Rightarrow Area=s^2=\frac{t^2}{2}$

Report an Error

View SSAT- Upper Level Tutors

Sarah
Certified Tutor

New York University, Bachelor of Fine Arts, Drama.

View SSAT- Upper Level Tutors

Peter
Certified Tutor

Nottingham University UK, Bachelor in Arts, Mathematics.

View SSAT- Upper Level Tutors

Kevin
Certified Tutor

St. Johns University, Bachelors, Math/Coaching.

All SSAT Upper Level Math Resources

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

Popular Subjects

ISEE Tutors in Houston, Chemistry Tutors in Atlanta, Algebra Tutors in Chicago, LSAT Tutors in Chicago, MCAT Tutors in Philadelphia, Algebra Tutors in New York City, ACT Tutors in Philadelphia, SSAT Tutors in Denver, GMAT Tutors in San Diego, SAT Tutors in San Diego

Popular Courses & Classes

SSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Denver, SAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Boston, SAT Courses & Classes in New York City, LSAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Philadelphia, MCAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Houston

Popular Test Prep

GRE Test Prep in Philadelphia, SAT Test Prep in Atlanta, MCAT Test Prep in Philadelphia, LSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Philadelphia, GRE Test Prep in Boston, ACT Test Prep in Boston, LSAT Test Prep in Washington DC, SAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Miami

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 : Area of Polygons

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 #10 : How To Find The Area Of A Pentagon

Example Question #982 : Ssat Upper Level Quantitative (Math)

Example Question #983 : Ssat Upper Level Quantitative (Math)

Example Question #11 : How To Find The Area Of A Pentagon

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

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

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

$4\sqrt{3}$

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

Example Question #4 : How To Find The Area Of A Square

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: