We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

Create An Account

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #64 : How To Find The Area Of A Square

Find the area of a square if its diagonal is $7\sqrt5$ .

Possible Answers:

$46\sqrt5$

$\frac{245\sqrt2}{4}$

$\frac{245}{2}$

$71\sqrt3$

Correct answer:

$\frac{245}{2}$

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(7\sqrt5)^2}{2}=\frac{245}{2}$

Report an Error

Example Question #65 : How To Find The Area Of A Square

Find the area of a square if its diagonal is $9\sqrt{10}$ .

Possible Answers:

$405\sqrt3$

405

$405\sqrt2$

$\frac{405}{2}$

Correct answer:

405

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(9\sqrt{10})^2}{2}=\frac{810}{2}=405$

Report an Error

Example Question #66 : How To Find The Area Of A Square

Find the area of a square if its diagonal is $7\sqrt{10}$ .

Possible Answers:

$490\sqrt2$

$\frac{245\sqrt3}{2}$

$\frac{245}{2}$

245

Correct answer:

245

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(7\sqrt{10})^2}{2}=\frac{490}{2}=245$

Report an Error

Example Question #67 : How To Find The Area Of A Square

Find the area of a square if its diagonal is $6\sqrt{10}$ .

Possible Answers:

180

$90\sqrt3$

$180\sqrt2$

$360\sqrt3$

Correct answer:

180

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(6\sqrt{10})^2}{2}=\frac{360}{2}=180$

Report an Error

Example Question #68 : How To Find The Area Of A Square

Find the area of a square if its diagonal is $8\sqrt{10}$ .

Possible Answers:

320

$320\sqrt3$

$320\sqrt2$

$160\sqrt3$

Correct answer:

320

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(8\sqrt{10})^2}{2}=\frac{640}{2}=320$

Report an Error

Example Question #69 : How To Find The Area Of A Square

Find the area of a square if its diagonal is $11\sqrt2$ .

Possible Answers:

$121\sqrt3$

$\frac{121\sqrt2}{2}$

$\frac{121}{2}$

121

Correct answer:

121

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(11\sqrt{2})^2}{2}=\frac{242}{2}=121$

Report an Error

Example Question #70 : How To Find The Area Of A Square

Find the area of a square if its diagonal is $15\sqrt{10}$ .

Possible Answers:

1125

2250

775

875

Correct answer:

1125

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(15\sqrt{10})^2}{2}=\frac{2250}{2}=1125$

Report an Error

Example Question #71 : How To Find The Area Of A Square

Find the area of a square if its diagonal is $12\sqrt{14}$ .

Possible Answers:

$1008\sqrt2$

$504\sqrt{3}$

1008

$1008\sqrt5$

Correct answer:

1008

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(12\sqrt{14})^2}{2}=\frac{2016}{2}=1008$

Report an Error

Example Question #72 : How To Find The Area Of A Square

Find the area of a square if its diagonal is $\sqrt{30}$ .

Possible Answers:

$30\sqrt2$

$15\sqrt2$

Correct answer:

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(\sqrt{30})^2}{2}=\frac{30}{2}=15$

Report an Error

Example Question #101 : Squares

Find the area of a square if its diagonal is $2\sqrt{15}$ .

Possible Answers:

$30\sqrt3$

$30\sqrt2$

Correct answer:

Explanation:

The diagonal of a square is also the hypotenuse of a 45-45-90 triangle.

Recall how to find the area of a square:

$\text{Area}=\text{side}^2$

Now, use the Pythagorean theorem to find the area of the square.

$\text{side}^2+\text{side}^2=\text{Diagonal}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{Area}=\text{side}^2=\frac{\text{Diagonal}^2}{2}$

Plug in the length of the diagonal to find the area of the square.

$\text{Area}=\frac{(2\sqrt{15})^2}{2}=\frac{60}{2}=30$

Report an Error

View Tutors

Richard
Certified Tutor

University of Chicago, Bachelor of Economics, Economics.

View Tutors

Brandon
Certified Tutor

Michigan State University, Bachelor of Science, Accounting.

View Tutors

Christine
Certified Tutor

California University of Pennsylvania, Bachelor of Science, Elementary School Teaching. Coastal Carolina University, Master o...

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in San Francisco-Bay Area, Statistics Tutors in Seattle, Statistics Tutors in Boston, Biology Tutors in Miami, LSAT Tutors in Philadelphia, LSAT Tutors in San Francisco-Bay Area, English Tutors in Phoenix, LSAT Tutors in Seattle, Chemistry Tutors in Philadelphia, Spanish Tutors in San Diego

Popular Courses & Classes

GRE Courses & Classes in New York City, SAT Courses & Classes in San Diego, LSAT Courses & Classes in Philadelphia, GRE Courses & Classes in Boston, SAT Courses & Classes in Washington DC, Spanish Courses & Classes in Miami, SAT Courses & Classes in Miami, GMAT Courses & Classes in New York City, ACT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in San Diego

Popular Test Prep

ACT Test Prep in San Diego, GRE Test Prep in Boston, ISEE Test Prep in Boston, LSAT Test Prep in Seattle, ACT Test Prep in San Francisco-Bay Area, SAT Test Prep in San Diego, GRE Test Prep in Phoenix, MCAT Test Prep in Phoenix, LSAT Test Prep in Chicago, GRE 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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #64 : How To Find The Area Of A Square

Example Question #65 : How To Find The Area Of A Square

Example Question #66 : How To Find The Area Of A Square

Example Question #67 : How To Find The Area Of A Square

Example Question #68 : How To Find The Area Of A Square

Example Question #69 : How To Find The Area Of A Square

Example Question #70 : How To Find The Area Of A Square

Example Question #71 : How To Find The Area Of A Square

Example Question #72 : How To Find The Area Of A Square

Example Question #101 : Squares

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: