Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : Basic 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 #111 : How To Find The Area Of A Circle

If a rectangle with a diagonal of is inscribed in a circle, what is the area of the circle?

Possible Answers:

$100\pi$

$40\pi$

$400\pi$

$20\pi$

Correct answer:

$100\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=20$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(20)$

Simplify.

$\text{radius}=10$

Finally, recall how to find the area of a circle:

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

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

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

Solve.

$\text{Area}=100\pi$

Report an Error

Example Question #112 : How To Find The Area Of A Circle

If a rectangle with a diagonal of is inscribed in a circle, what is the area of the circle?

Possible Answers:

$196\pi$

$49\pi$

$28\pi$

$241\pi$

Correct answer:

$49\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=14$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(14)$

Simplify.

$\text{radius}=7$

Finally, recall how to find the area of a circle:

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

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

$\text{Area}=\pi\times(7)^2$

Solve.

$\text{Area}=49\pi$

Report an Error

Example Question #113 : How To Find The Area Of A Circle

If a rectangle with a diagonal of $6\sqrt3$ is inscribed in a circle, what is the area of the circle?

Possible Answers:

$54\pi$

$27\pi$

$6\sqrt3\pi$

$54\pi$

Correct answer:

$27\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=6\sqrt3$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(6\sqrt3)$

Simplify.

$\text{radius}=3\sqrt3$

Finally, recall how to find the area of a circle:

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

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

$\text{Area}=\pi\times(3\sqrt3)^2$

Solve.

$\text{Area}=27\pi$

Report an Error

Example Question #111 : Plane Geometry

If a rectangle with a diagonal of $18\sqrt2$ is inscribed in a circle, what is the area of the circle?

Possible Answers:

$18\sqrt2\pi$

$162\pi$

$81\pi$

$72\pi$

Correct answer:

$162\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=18\sqrt2$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(18\sqrt2)$

Simplify.

$\text{radius}=9\sqrt2$

Finally, recall how to find the area of a circle:

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

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

$\text{Area}=\pi\times(9\sqrt2)^2$

Solve.

$\text{Area}=162\pi$

Report an Error

Example Question #114 : How To Find The Area Of A Circle

If a rectangle with a diagonal of $16\sqrt3$ is inscribed in a circle, what is the area of the circle?

Possible Answers:

$16\sqrt3\pi$

$81\pi$

$192\pi$

$32\sqrt2\pi$

Correct answer:

$192\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=16\sqrt3$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(16\sqrt3)$

Simplify.

$\text{radius}=8\sqrt3$

Finally, recall how to find the area of a circle:

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

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

$\text{Area}=\pi\times(8\sqrt3)^2$

Solve.

$\text{Area}=192\pi$

Report an Error

Example Question #112 : Plane Geometry

A rectangle with a diagonal of $2\sqrt{13}$ is incribed in a circle, what is the area of the circle?

Possible Answers:

$39\pi$

$26\pi$

$13\pi$

$52\pi$

Correct answer:

$13\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=2\sqrt{13}$

Now, recall the relationship between the diameter of a circle and its radius:

$\text{radius}=\frac{1}{2}(\text{Diameter})$

Substitute in the given diameter to find the radius of the circle.

$\text{radius}=\frac{1}{2}(2\sqrt{13})$

Simplify.

$\text{radius}=\sqrt{13}$

Finally, recall how to find the area of a circle:

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

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

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

Solve.

$\text{Area}=13\pi$

Report an Error

Example Question #111 : How To Find The Area Of A Circle

Find the area of a circle given radius is x^3 .

Possible Answers:

$x^2\pi$

$x^6\pi$

$x^5\pi$

$x^3\pi$

Correct answer:

$x^6\pi$

Explanation:

To solve, simply use the formula for the area of a circle.

Given the radius is x^3 , substitute it in for r in the below formula.

Also recall the rules of exponents which states that when an exponent is raised to another exponent, they are multiplied together.

$(x^n)^m=x^{m\cdot n}$

Thus,

$A=\pi{r^2}=\pi*(x^3)^2=\pi*x^{3*2}=x^6\pi$

Report an Error

Example Question #111 : Basic Geometry

Find the area of a circle given a radius of 3.

Possible Answers:

$27\pi$

$\frac{9}{2}\pi$

$6\pi$

$9\pi$

Correct answer:

$9\pi$

Explanation:

To solve, simply use the formula for the area of a circle.

Thus,

given, r=3

$A=\pi{r^2}=\pi*3^2=9\pi$ .

Report an Error

Example Question #112 : Basic Geometry

In the figure below, a circle is inscribed in a square. If the side length of the square is , what is the area of the shaded region?

Possible Answers:

0.96

0.86

0.88

1.04

Correct answer:

0.86

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

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

Plug in the given value to find the area of the square.

$\text{Area of Square}=2^2=4$

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

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

Plug in the value of the diameter to find the length of the radius.

$\text{Radius}=\frac{2}{2}=1$

Now, recall the formula to find the area of a circle:

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

Plug in the value of the radius to find the area of the circle.

$\text{Area of Circle}=\pi\times 1^2=\pi$

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

$\text{Area of Shaded Region}=\text{Area of Square}-\text{Area of Circle}$

$\text{Area of Shaded Region}=4-\pi=0.86$

Round to two places after the decimal.

Report an Error

Example Question #113 : Basic Geometry

In the figure below, a circle is inscribed in a square. If the length of a side of the square is , what is the area of the shaded region?

Possible Answers:

3.34

3.43

3.19

3.67

Correct answer:

3.43

Explanation:

From the figure, you should notice that the side length of the square is also the same as the length of the diameter of the circle.

To find the area of the shaded region, we will need to subtract the area of the circle from the area of the square.

First, recall how to find the area of a square:

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

Plug in the given value to find the area of the square.

$\text{Area of Square}=4^2=16$

Now, find the area of the circle.

We will need to first find the length of the radius of the circle.

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

Plug in the value of the diameter to find the length of the radius.

$\text{Radius}=\frac{4}{2}=2$

Now, recall the formula to find the area of a circle:

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

Plug in the value of the radius to find the area of the circle.

$\text{Area of Circle}=\pi\times 2^2=4\pi$

Now, to find the area of the shaded region, subtract the area of the circle from the area of the square.

$\text{Area of Shaded Region}=\text{Area of Square}-\text{Area of Circle}$

$\text{Area of Shaded Region}=16-4\pi=3.43$

Round to two places after the decimal.

Report an Error

View Tutors

Rommel
Certified Tutor

STI-Gensan College, Bachelor of Science, Information Technology. Brokenshire College Socsksargen, INC., Bachelor of Education...

View Tutors

Brigette
Certified Tutor

William Carey University, Masters in Education, Elementary School Teaching.

View Tutors

Blanca
Certified Tutor

University of Phoenix-Tucson Campus, Bachelor of Science, Business Administration and Management.

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, Calculus Tutors in Miami, Reading Tutors in San Diego, SAT Tutors in New York City, Computer Science Tutors in Washington DC, GRE Tutors in Chicago, GRE Tutors in Atlanta, GMAT Tutors in Houston, Calculus Tutors in Boston, SAT Tutors in Phoenix

Popular Courses & Classes

LSAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Atlanta, ISEE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Houston, Spanish Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Washington DC, MCAT Courses & Classes in New York City, SSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in New York City, SAT Courses & Classes in Washington DC

Popular Test Prep

SSAT Test Prep in Los Angeles, GRE Test Prep in Seattle, MCAT Test Prep in Houston, GRE Test Prep in Los Angeles, ACT Test Prep in Miami, LSAT Test Prep in New York City, ISEE Test Prep in San Francisco-Bay Area, ACT Test Prep in New York City, SSAT Test Prep in Washington DC, MCAT Test Prep in Philadelphia

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 : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #111 : How To Find The Area Of A Circle

Example Question #112 : How To Find The Area Of A Circle

Example Question #113 : How To Find The Area Of A Circle

Example Question #111 : Plane Geometry

Example Question #114 : How To Find The Area Of A Circle

Example Question #112 : Plane Geometry

Example Question #111 : How To Find The Area Of A Circle

Example Question #111 : Basic Geometry

Example Question #112 : Basic Geometry

Example Question #113 : Basic Geometry

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: