Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Triangles

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #261 : Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Possible Answers:

79.77

72.30

75.78

82.30

Correct answer:

75.78

Explanation:

Recall that a regular hexagon can be divided into congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

Plug in the length of a side of the equilateral triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{5})^2}{4}=\frac{25\sqrt3}{4}$

Now, multiply this area by to find the area of the entire figure.

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(\frac{25\sqrt3}{4})=75.78$

Make sure to round to places after the decimal.

Report an Error

Example Question #262 : Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Possible Answers:

109.12

112.59

104.97

120.41

Correct answer:

109.12

Explanation:

Recall that a regular hexagon can be divided into congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

Plug in the length of a side of the equilateral triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(6)^2}{4}=\frac{36\sqrt3}{4}=9\sqrt3$

Now, multiply this area by to find the area of the entire figure.

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(9\sqrt3)=109.12$

Make sure to round to places after the decimal.

Report an Error

Example Question #263 : Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Possible Answers:

185.23

176.58

198.41

193.99

Correct answer:

193.99

Explanation:

Recall that a regular hexagon can be divided into congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

Plug in the length of a side of the equilateral triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(8)^2}{4}=\frac{64\sqrt3}{4}=16\sqrt3$

Now, multiply this area by to find the area of the entire figure.

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(16\sqrt3)=193.99$

Make sure to round to places after the decimal.

Report an Error

Example Question #703 : Plane Geometry

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Possible Answers:

501.28

436.48

421.82

491.50

Correct answer:

436.48

Explanation:

Recall that a regular hexagon can be divided into congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

Plug in the length of a side of the equilateral triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(12)^2}{4}=\frac{144\sqrt3}{4}=36\sqrt3$

Now, multiply this area by to find the area of the entire figure.

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(36\sqrt3)=436.48$

Make sure to round to places after the decimal.

Report an Error

Example Question #265 : Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Possible Answers:

775.96

741.22

770.29

772.11

Correct answer:

775.96

Explanation:

Recall that a regular hexagon can be divided into congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

Plug in the length of a side of the equilateral triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(16)^2}{4}=\frac{256\sqrt3}{4}=64\sqrt3$

Now, multiply this area by to find the area of the entire figure.

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(64\sqrt3)=775.96$

Make sure to round to places after the decimal.

Report an Error

Example Question #41 : How To Find The Area Of An Equilateral Triangle

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Possible Answers:

1298.41

1122.01

1145.29

1212.44

Correct answer:

1212.44

Explanation:

Recall that a regular hexagon can be divided into congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

Plug in the length of a side of the equilateral triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(20)^2}{4}=\frac{400\sqrt3}{4}=100\sqrt3$

Now, multiply this area by to find the area of the entire figure.

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(100\sqrt3)=1212.44$

Make sure to round to places after the decimal.

Report an Error

Example Question #42 : How To Find The Area Of An Equilateral Triangle

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Possible Answers:

1500.67

1682.52

1721.40

1745.91

Correct answer:

1745.91

Explanation:

Recall that a regular hexagon can be divided into congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

Plug in the length of a side of the equilateral triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(24)^2}{4}=\frac{576\sqrt3}{4}=144\sqrt3$

Now, multiply this area by to find the area of the entire figure.

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(144\sqrt3)=1745.91$

Make sure to round to places after the decimal.

Report an Error

Example Question #61 : Equilateral Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Possible Answers:

2424.54

2149.20

2205.29

2376.37

Correct answer:

2376.37

Explanation:

Recall that a regular hexagon can be divided into congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

Plug in the length of a side of the equilateral triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(28)^2}{4}=\frac{784\sqrt3}{4}=196\sqrt3$

Now, multiply this area by to find the area of the entire figure.

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(196\sqrt3)=2376.37$

Make sure to round to places after the decimal.

Report an Error

Example Question #261 : Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Possible Answers:

3098.59

2790.18

3199.26

3103.84

Correct answer:

3103.84

Explanation:

Recall that a regular hexagon can be divided into congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

Plug in the length of a side of the equilateral triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(32)^2}{4}=\frac{1024\sqrt3}{4}=256\sqrt3$

Now, multiply this area by to find the area of the entire figure.

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(256\sqrt3)=3103.84$

Make sure to round to places after the decimal.

Report an Error

Example Question #62 : Equilateral Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Possible Answers:

3612.06

3938.29

4510.20

3782.09

Correct answer:

3938.29

Explanation:

Recall that a regular hexagon can be divided into congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(\text{side})^2}{4}$

Plug in the length of a side of the equilateral triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3(36)^2}{4}=\frac{1296\sqrt3}{4}=324\sqrt3$

Now, multiply this area by to find the area of the entire figure.

$\text{Area of Figure}=7(\text{Area of Equilateral Triangle})$

$\text{Area of Figure}=7(324\sqrt3)=3928.29$

Make sure to round to places after the decimal.

Report an Error

View Tutors

Sujay
Certified Tutor

View Tutors

Melissa
Certified Tutor

University of Houston, Bachelors, Political Science and Government.

View Tutors

Adam
Certified Tutor

Boston University, Bachelor of Education, Education. Johns Hopkins University, Masters in Education, Education.

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Chicago, Algebra Tutors in Washington DC, SSAT Tutors in Houston, MCAT Tutors in Atlanta, ISEE Tutors in San Francisco-Bay Area, Algebra Tutors in Chicago, English Tutors in Atlanta, Physics Tutors in Denver, LSAT Tutors in Seattle, LSAT Tutors in Philadelphia

Popular Courses & Classes

GRE Courses & Classes in Denver, GRE Courses & Classes in Phoenix, SSAT Courses & Classes in Phoenix, GRE Courses & Classes in Washington DC, MCAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Washington DC, SSAT Courses & Classes in New York City, ACT Courses & Classes in Phoenix, ISEE Courses & Classes in Phoenix

Popular Test Prep

MCAT Test Prep in New York City, ISEE Test Prep in Philadelphia, GRE Test Prep in Miami, MCAT Test Prep in Houston, LSAT Test Prep in New York City, MCAT Test Prep in Boston, GRE Test Prep in Denver, GRE Test Prep in Phoenix, LSAT Test Prep in Philadelphia, 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

Intermediate Geometry : Triangles

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #261 : Triangles

Example Question #262 : Triangles

Example Question #263 : Triangles

Example Question #703 : Plane Geometry

Example Question #265 : Triangles

Example Question #41 : How To Find The Area Of An Equilateral Triangle

Example Question #42 : How To Find The Area Of An Equilateral Triangle

Example Question #61 : Equilateral Triangles

Example Question #261 : Triangles

Example Question #62 : Equilateral Triangles

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: