We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : Plane Geometry

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 #61 : Radius

A circle is inscribed in a square that has an area of 400 . What is the area of the circle?

Possible Answers:

100

$200\pi$

150

$100\pi$

Correct answer:

$100\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{400}=20$

$\text{side length}=\text{diameter}=20$

Now, recall how to find the area of a circle.

$\text{Area of circle}=\pi\times\text{radius}^2$

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{20}{2}=10$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times 10^2=100\pi$

Report an Error

Example Question #62 : How To Find The Area Of A Circle

A circle is inscribed in a square that has an area of 784 . What is the area of the circle?

Possible Answers:

$216\pi$

$148\pi$

$196\pi$

$122\pi$

Correct answer:

$196\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{784}=28$

$\text{side length}=\text{diameter}=28$

Now, recall how to find the area of a circle.

$\text{Area of circle}=\pi\times\text{radius}^2$

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{28}{2}=14$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times 14^2=196\pi$

Report an Error

Example Question #63 : How To Find The Area Of A Circle

A circle is inscribed in a square that has an area of 324 . What is the area of the circle?

Possible Answers:

$90\pi$

$81\pi$

$128\pi$

Correct answer:

$81\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{324}=18$

$\text{side length}=\text{diameter}=18$

Now, recall how to find the area of a circle.

$\text{Area of circle}=\pi\times\text{radius}^2$

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{18}{2}=9$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times 9^2=81\pi$

Report an Error

Example Question #61 : Basic Geometry

A circle is inscribed in a square that has an area of 484 . What is the area of the circle?

Possible Answers:

$121\pi$

$100\pi$

$144\pi$

Correct answer:

$121\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{484}=22$

$\text{side length}=\text{diameter}=22$

Now, recall how to find the area of a circle.

$\text{Area of circle}=\pi\times\text{radius}^2$

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{22}{2}=11$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times 11^2=121\pi$

Report an Error

Example Question #61 : Radius

A circle is inscribed in a square that has an area of $\frac{1}{4}$ . What is the area of the circle?

Possible Answers:

$\frac{\pi}{32}$

$\frac{\pi}{16}$

$\frac{\pi}{4}$

$\frac{\pi}{8}$

Correct answer:

$\frac{\pi}{16}$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{\frac{1}{4}}=\frac{1}{2}$

$\text{side length}=\text{diameter}=\frac{1}{2}$

Now, recall how to find the area of a circle.

$\text{Area of circle}=\pi\times\text{radius}^2$

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{\frac{1}{2}}{2}=\frac{1}{4}$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times (\frac{1}{4})^2=\frac{\pi}{16}$

Report an Error

Example Question #65 : Radius

A circle is inscribed in a square that has an area of 1024 . What is the area of the circle?

Possible Answers:

$200\pi$

$256\pi$

$164\pi$

$212\pi$

Correct answer:

$256\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{1024}=32$

$\text{side length}=\text{diameter}=32$

Now, recall how to find the area of a circle.

$\text{Area of circle}=\pi\times\text{radius}^2$

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{32}{2}=16$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times 14^2=256\pi$

Report an Error

Example Question #62 : Basic Geometry

A circle is inscribed in a square that has an area of 900 . What is the area of the circle?

Possible Answers:

$275\pi$

$225\pi$

$30\pi$

$300\pi$

Correct answer:

$225\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{900}=30$

$\text{side length}=\text{diameter}=30$

Now, recall how to find the area of a circle.

$\text{Area of circle}=\pi\times\text{radius}^2$

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{30}{2}=15$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times 15^2=225\pi$

Report an Error

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

Find the area of the circle with the given diameter.

Possible Answers:

$24\pi$

$168\pi$

$144\pi$

$240\pi$

Correct answer:

$144\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

Substitute in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{24}{2}$

Simplify.

$\text{Radius}=12$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 12^2$

Solve.

$\text{Area}=144\pi$

Report an Error

Example Question #61 : Plane Geometry

Find the area of the circle with the given diameter.

Possible Answers:

$169\pi$

$338\pi$

$676\pi$

$104\pi$

Correct answer:

$169\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

Substitute in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{26}{2}$

Simplify.

$\text{Radius}=13$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 13^2$

Solve.

$\text{Area}=169\pi$

Report an Error

Example Question #62 : Radius

Find the area of the circle with the given diameter.

Possible Answers:

$196\pi$

$140\pi$

$170\pi$

$156\pi$

Correct answer:

$196\pi$

Explanation:

Recall how to find the area of a circle.

$\text{Area}=\pi\times\text{radius}^2$

Now, since we have the diameter, recall the relationship between the radius and the diameter.

$\text{Radius}=\frac{\text{Diameter}}{2}$

Substitute in the value of the diameter to find the value of the radius.

$\text{Radius}=\frac{28}{2}$

Simplify.

$\text{Radius}=14$

Substitute in the value of the radius to find the area.

$\text{Area}=\pi\times 14^2$

Solve.

$\text{Area}=196\pi$

Report an Error

View Tutors

Adair
Certified Tutor

Marymount College, Bachelor of Science, Chemistry.

View Tutors

Paarth
Certified Tutor

New Jersey Institute of Technology, Bachelor of Science, Computer Science.

View Tutors

Joshua
Certified Tutor

Murray State University, Bachelor in Arts, Spanish. Lipscomb University, Bachelor of Science, Teacher Assistant.

All Basic Geometry Resources

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

Popular Subjects

Computer Science Tutors in Seattle, Reading Tutors in Seattle, Math Tutors in San Francisco-Bay Area, English Tutors in Philadelphia, MCAT Tutors in Los Angeles, Reading Tutors in Atlanta, GMAT Tutors in Chicago, French Tutors in Phoenix, Biology Tutors in Philadelphia, Statistics Tutors in Houston

Popular Courses & Classes

ISEE Courses & Classes in San Diego, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in New York City, MCAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Los Angeles, LSAT Courses & Classes in New York City, GMAT Courses & Classes in Washington DC, ACT Courses & Classes in Houston, LSAT Courses & Classes in Houston, ISEE Courses & Classes in Seattle

Popular Test Prep

GRE Test Prep in Phoenix, GRE Test Prep in Washington DC, SSAT Test Prep in Atlanta, ISEE Test Prep in Philadelphia, LSAT Test Prep in New York City, MCAT Test Prep in San Diego, MCAT Test Prep in New York City, GRE Test Prep in Denver, LSAT Test Prep in Miami, 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 : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #61 : Radius

Example Question #62 : How To Find The Area Of A Circle

Example Question #63 : How To Find The Area Of A Circle

Example Question #61 : Basic Geometry

Example Question #61 : Radius

Example Question #65 : Radius

Example Question #62 : Basic Geometry

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

Example Question #61 : Plane Geometry

Example Question #62 : Radius

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: