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 #899 : Basic Geometry

Find the perimeter of a square inscribed in a circle that has a diameter of $14\sqrt3$ .

Possible Answers:

$28\sqrt5$

$28\sqrt2$

$28\sqrt6$

Correct answer:

$28\sqrt6$

Explanation:

Notice that the diameter of the circle is also the diagonal of the square. The diagonal of the square is also the hypotenuse of a right isosceles triangle that has the sides of the square as its legs.

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{14\sqrt3(\sqrt2)}{2}$

Simplify.

$\text{side}=7\sqrt6$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(7\sqrt6)$

Solve.

$\text{Perimeter}=28\sqrt6$

Report an Error

Example Question #900 : Basic Geometry

Find the perimeter of a square inscribed in a circle that has a diameter of 100 .

Possible Answers:

$400\sqrt2$

$200\sqrt2$

10000

$100\sqrt2$

Correct answer:

$200\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{100(\sqrt2)}{2}$

Simplify.

$\text{side}=50\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(50\sqrt2)$

Solve.

$\text{Perimeter}=200\sqrt2$

Report an Error

Example Question #491 : Quadrilaterals

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

200

160

$80\sqrt2$

$40\sqrt2$

Correct answer:

$80\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{40(\sqrt2)}{2}$

Simplify.

$\text{side}=20\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(20\sqrt2)$

Solve.

$\text{Perimeter}=80\sqrt2$

Report an Error

Example Question #492 : Quadrilaterals

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

176

$44\sqrt2$

$88\sqrt2$

$132\sqrt2$

Correct answer:

$88\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{44(\sqrt2)}{2}$

Simplify.

$\text{side}=22\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(22\sqrt2)$

Solve.

$\text{Perimeter}=88\sqrt2$

Report an Error

Example Question #493 : Quadrilaterals

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

$120\sqrt2$

$180\sqrt2$

$60\sqrt2$

240

Correct answer:

$120\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{60(\sqrt2)}{2}$

Simplify.

$\text{side}=30\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(30\sqrt2)$

Solve.

$\text{Perimeter}=120\sqrt2$

Report an Error

Example Question #494 : Quadrilaterals

Find the perimeter of a square inscribed in a circle that has a diameter of .

Possible Answers:

$152\sqrt2$

$144\sqrt2$

304

$76\sqrt2$

Correct answer:

$152\sqrt2$

Explanation:

$\text{diameter}=\text{diagonal}$

Now, use the Pythagorean theorem to find the length of the sides of the square.

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

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

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Now, substitute in the value of the diagonal to find the length of a side of the square.

$\text{side}=\frac{76(\sqrt2)}{2}$

Simplify.

$\text{side}=38\sqrt2$

Now, recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side})$

Substitute in the value of the side to find the perimeter of the square.

$\text{Perimeter}=4(38\sqrt2)$

Solve.

$\text{Perimeter}=152\sqrt2$

Report an Error

Example Question #51 : How To Find The Perimeter Of A Square

Find the perimeter of a square whose side length is 7.

Possible Answers:

Correct answer:

Explanation:

The perimeter of a square is found by adding all the side lengths together. In a square there are two widths, two lengths, and they are equal.

In other words, simply use the formula for the perimeter of a square and let,

To solve, simply use the formula for the perimeter of a square let,

s=7

thus,

P=4s=4*7=28 .

Report an Error

Example Question #61 : How To Find The Perimeter Of A Square

Find the perimeter of a square with side length 2.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a square. Thus,

A=4s=4*2=8

Report an Error

Example Question #62 : How To Find The Perimeter Of A Square

Find the perimeter of a square with side length of 2.

Possible Answers:

$2\sqrt2$

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a square. Thus,

P=4s=4*2=8

If the formula escapes you, simply sum the sides. However, you must know that all the sides in a square are equal in order to add them up. Since they are equal, the formula just shows you that you can multiply one side by 4 instead of adding them all together.

Report an Error

Example Question #61 : How To Find The Perimeter Of A Square

A square garden was made to put 8 plants that are 1.25 feet wide each on each side. The corner plants were included in two sides. What is the length of the perimeter?

Possible Answers:

40ft

10ft

30ft

50ft

20ft

Correct answer:

40ft

Explanation:

Each side would be 10 feet long. A square has 4 sides.

The perimeter of a square is all the sides added together.

P=s_1+s_2+s_3+s_4

Since all the sides are equal in a square we can rewrite the equation to be,

P=4s .

Given

s=10 ,

10 * 4 = 40

Therefore the perimeter is 40ft.

Report an Error

View Tutors

Maria
Certified Tutor

University of South Florida-Main Campus, Bachelor of Science, Finance.

View Tutors

PV
Certified Tutor

Abilene Christian University, Bachelor of Science, Engineering Physics.

View Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

All Basic Geometry Resources

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

Popular Subjects

Computer Science Tutors in Los Angeles, Computer Science Tutors in Boston, Biology Tutors in Washington DC, English Tutors in Seattle, MCAT Tutors in Miami, GMAT Tutors in Denver, SSAT Tutors in San Diego, Math Tutors in Denver, Calculus Tutors in Denver, MCAT Tutors in Philadelphia

Popular Courses & Classes

LSAT Courses & Classes in Atlanta, SSAT Courses & Classes in New York City, GMAT Courses & Classes in Boston, Spanish Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in San Diego, GRE Courses & Classes in Denver, ACT Courses & Classes in Phoenix, ACT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in New York City, ISEE Courses & Classes in New York City

Popular Test Prep

ACT Test Prep in Phoenix, LSAT Test Prep in Boston, SSAT Test Prep in Chicago, SSAT Test Prep in Philadelphia, ACT Test Prep in San Francisco-Bay Area, GRE Test Prep in San Diego, LSAT Test Prep in Houston, GRE Test Prep in Chicago, GMAT Test Prep in Dallas Fort Worth, ISEE 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

Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #899 : Basic Geometry

Example Question #900 : Basic Geometry

Example Question #491 : Quadrilaterals

Example Question #492 : Quadrilaterals

Example Question #493 : Quadrilaterals

Example Question #494 : Quadrilaterals

Example Question #51 : How To Find The Perimeter Of A Square

Example Question #61 : How To Find The Perimeter Of A Square

Example Question #62 : How To Find The Perimeter Of A Square

Example Question #61 : How To Find The Perimeter Of A Square

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: