We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Geometry

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

Find the area of the shaded region:

Possible Answers:

$30 \pi\ m^2$

$32 \pi\ m^2$

$24 \pi\ m^2$

$26 \pi\ m^2$

$28 \pi\ m^2$

Correct answer:

$28 \pi\ m^2$

Explanation:

The formula for the area of the shaded region is

$A = A_{large circle}-A_{small circle}= \pi r_{large}^2 - \pi r_{small}^2,$

where is the radius of the circle.

Plugging in our values, we get:

$A = \pi (8\ m)^2 - \pi (6\ m)^2$

$A = 28 \pi\ m^2$

Report an Error

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

Find the area of the following octagon:

Possible Answers:

$288\sqrt{2}+288\ m^2$

$200\sqrt{2}+288\ m^2$

$288\sqrt{2}+280\ m^2$

$280\sqrt{2}+288\ m^2$

$280\sqrt{2}+280\ m^2$

Correct answer:

$288\sqrt{2}+288\ m^2$

Explanation:

The formula for the area of a regular octagon is:

$A = \frac{1}{2}(perimeter)(apothem)$

Plugging in our values, we get:

$A = \frac{1}{2}(96\ m)(6\sqrt{2}\ m+6\ m)$

$A = 288\sqrt{2}+288\ m^2$

Report an Error

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

Find the area of a rectangle with a base of (x + 3) and a width of (x - 3) in terms of .

Possible Answers:

$x^{2 } - 3x - 9$

$x^{2 } + 9$

$x^{2}$

none of the other answers

$x^{2} - 9$

Correct answer:

$x^{2} - 9$

Explanation:

This problem simply becomes a matter of FOILing (first outer inner last)

The area of the shape is Base times Height.

So, multiplying (x + 3) and (x - 3) using FOIL, we get an area of $x^{2} - 9$

Report an Error

Example Question #11 : Plane Geometry

Find the area of a square whose diagonal is .

Possible Answers:

144

none of these answers

Correct answer:

Explanation:

If the diagonal of a square is , we can use the pythagorean theorem to solve for the length of the sides.

= length of side of the square

Doing so, we get $2x^{2} = 144$

$x = \sqrt{72}$

To find the area of the square, we square , resulting in .

Report an Error

Example Question #11 : Geometry

What is the magnitude of the interior angle of a regular nonagon?

Possible Answers:

140^o

144^o

135^o

129^o

Correct answer:

140^o

Explanation:

The equation to calculate the magnitude of an interior angle is $\frac{180(n-2)}{n}=int\ angle$ , where is equal to the number of sides.

For our question, n=9 .

$int\ angle= \frac{180(9-2)}{9}=\frac{(180)(7)}{9}=140^o$

Report an Error

Example Question #12 : Other Polygons

What is the interior angle measure of any regular heptagon?

Possible Answers:

135

130.2

128.6

125.8

Correct answer:

128.6

Explanation:

To find the angle of any regular polygon you find the number of sides, . In this example, n=7 .

You then subtract 2 from the number of sides yielding 5.

Take 5 and multiply it by 180 degrees to yield the total number of degrees in the regular heptagon. 5*180=900

Then to find one individual angle we divide 900 by the total number of angles, 7.

$\frac{900}{7}=128.6$

The answer is 128.6 .

Report an Error

Example Question #13 : Other Polygons

A regular polygon with sides has exterior angles that measure $1.5^{\circ }$ each. How many sides does the polygon have?

Possible Answers:

120

180

This figure cannot exist.

240

150

Correct answer:

240

Explanation:

The sum of the exterior angles of any polygon, one per vertex, is $360 ^{\circ }$ . As each angle measures $1.5^{\circ }$ , just divide 360 by 1.5 to get the number of angles.

$360 \div 1.5=240$

Report an Error

Example Question #14 : Other Polygons

What is the interior angle measure of any regular nonagon?

Possible Answers:

$140^{\circ}$

$120^{\circ}$

$200^{\circ}$

$160^{\circ}$

Correct answer:

$140^{\circ}$

Explanation:

To find the angle of any regular polygon you find the number of sides , which in this example is .

You then subtract from the number of sides yielding .

Take and multiply it by 180 degrees to yield a total number of degrees in the regular nonagon.

7*180=1260

Then to find one individual angle we divide 1260 by the total number of angles .

$\frac{1260}{9}=140$

The answer is 140 .

Report an Error

Example Question #2 : How To Find An Angle In A Polygon

What is the measure of one exterior angle of a regular seventeen-sided polygon (nearest tenth of a degree)?

Possible Answers:

$25.2 ^{\circ }$

$15.9^{\circ }$

$34.0 ^{\circ }$

$21.2^{\circ }$

$10.6^{\circ }$

Correct answer:

$21.2^{\circ }$

Explanation:

The sum of the measures of the exterior angles of any polygon, one per vertex, is $360^{\circ}$ . In a regular polygon, all of these angles are congruent, so divide 360 by 17 to get the measure of one exterior angle:

$360 \div 17 \approx 21.2^{\circ }$

Report an Error

Example Question #2 : How To Find An Angle In A Polygon

What is the measure of one exterior angle of a regular twenty-three-sided polygon (nearest tenth of a degree)?

Possible Answers:

$15.7 ^{\circ }$

$7.8^{\circ }$

$14.4^{\circ }$

$28.8^{\circ }$

$31.3^{\circ }$

Correct answer:

$15.7 ^{\circ }$

Explanation:

The sum of the measures of the exterior angles of any polygon, one per vertex, is $360^{\circ}$ . In a regular polygon, all of these angles are congruent, so divide 360 by 23 to get the measure of one exterior angle:

$360 \div 23 \approx 15.7 ^{\circ }$

Report an Error

View Tutors

Kaylee
Certified Tutor

Brigham Young University, Bachelor, MFA - Animation.

View Tutors

Angela
Certified Tutor

North Georgia College State University, Bachelor of Science, Special Education. North Georgia College State University, Mas...

View Tutors

Dereika
Certified Tutor

Southern University and A & M College, Bachelor of Science, Accounting. Grand Canyon University, Master of Science, Accounting.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Dallas Fort Worth, SAT Tutors in New York City, English Tutors in Los Angeles, English Tutors in Phoenix, SSAT Tutors in Denver, Math Tutors in San Francisco-Bay Area, Spanish Tutors in Miami, Physics Tutors in Boston, Spanish Tutors in Washington DC, SSAT Tutors in Miami

Popular Courses & Classes

SSAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Denver, SAT Courses & Classes in Chicago, Spanish Courses & Classes in Chicago, SSAT Courses & Classes in Boston, LSAT Courses & Classes in Denver, SSAT Courses & Classes in Houston, ISEE Courses & Classes in Seattle, SAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Houston

Popular Test Prep

SAT Test Prep in Seattle, GMAT Test Prep in Los Angeles, LSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in San Diego, ACT Test Prep in Philadelphia, SAT Test Prep in Denver, GMAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Houston, SAT Test Prep in Dallas Fort Worth, SAT Test Prep in Houston

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

High School Math : Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

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

Example Question #11 : Plane Geometry

Example Question #11 : Geometry

Example Question #12 : Other Polygons

Example Question #13 : Other Polygons

Example Question #14 : Other Polygons

Example Question #2 : How To Find An Angle In A Polygon

Example Question #2 : How To Find An Angle In A Polygon

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: