We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Parallelograms

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 #1 : Parallelograms

The length of a parallelogram is cm and the width is cm. One of its diagonals measures cm. Find the length of the other diagonal.

Possible Answers:

$2\sqrt{38}cm$

$4\sqrt{38}cm$

$3\sqrt{3}cm$

$\sqrt{142}cm$

None of the other answers.

Correct answer:

$\sqrt{142}cm$

Explanation:

The formula for the relationship between diagonals and sides of a parallologram is

$(d_{1})^{2} + (d_{2})^{2} = 2a^{2} + 2b^{2}$ ,

where $d_{1}$ represents one diagonal,

$d_{2}$ represents the other diagonal,

represents a side, and

represents the adjoining side.

So, in this problem, substitute the known values and solve for the missing diagonal.

$14^{2} + (d_{2})^{2} = 2(12)^{2} + 2(5)^{2} \rightarrow 196 + d^{2} = 288 + 50$

$\rightarrow d^{2} = 142 \rightarrow d = \sqrt{142}$

So, the missing diagonal is $\sqrt{142}$ cm.

Report an Error

Example Question #1 : How To Find The Length Of The Diagonal Of A Parallelogram

In the parallogram above, find the length of the labeled diagonal.

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

In a parallogram, diagonals bisect one another, thus you can set the two segments that are labeled in the picture equal to one another, then solve for .

So,

$2x - 2 = x + 12 \rightarrow x = 14$ .

If x = 14 , then you can substitute 14 into each labeled segment, to get a total of 52.

2(14)-2+14+12

28-2+14+12=52

Report an Error

Example Question #3 : Parallelograms

In the parallogram below, find the length of the labeled diagonal.

Parallelogram2

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

In a parallelogram, the diagonals bisect one another, so you can set the labeled segments equal to each other and then solve for .

$x + 14 = 5x - 10 \rightarrow 24 = 4x \rightarrow 6 = x$ .

If x = 6 , then you substitute 6 into each labeled segment, to get a total of 40.

6+14+5(6)-10

20+30-10=40

Report an Error

Example Question #4 : Parallelograms

Para3

In the parallelogram above, find the length of the labeled diagonal.

Possible Answers:

11.2

5.6

9.6

None of the other answers.

4.8

Correct answer:

11.2

Explanation:

In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to one another and then solve for .

$20 - 3x = 2x - 4 \rightarrow 24 = 5x \rightarrow 4.8 = x$ .

Then, substitute 4.8 for in each labeled segment to get a total of 11.2 for the diagonal length.

20-3(4.8)+2(4.8)-4

20-14.4+9.6-4=11.2

Report an Error

Example Question #2 : How To Find The Length Of The Diagonal Of A Parallelogram

Suppose a square has an area of 6. What is the diagonal of the parallelogram?

Possible Answers:

$3\sqrt3$

$\frac{3\sqrt2}{2}$

$6\sqrt2$

$2\sqrt3$

$3\sqrt2$

Correct answer:

$2\sqrt3$

Explanation:

Write the formula to find the side of the square given the area.

A=s^2

Find the side.

6=s^2

$s=\sqrt6$

The diagonal of the square can be solved by using the Pythagorean Theorem.

a^2+b^2=c^2

$a=b=s=\sqrt6$

Substitute and solve for the diagonal, .

$(\sqrt6)^2+(\sqrt6)^2 =c^2$

6+6=c^2

c^2=12

$c=\sqrt{12}=2\sqrt3$

Report an Error

Example Question #5 : Parallelograms

If the side length of a square is , what is the diagonal of the square?

Possible Answers:

$a^2\sqrt6$

$3a\sqrt2$

$9a\sqrt2$

$3a^2\sqrt2$

$a\sqrt6$

Correct answer:

$3a\sqrt2$

Explanation:

Write the diagonal formula for a square.

$d=s\sqrt2$

Substitute the side length and reduce.

$d=3a\sqrt2$

Report an Error

Example Question #1 : How To Find The Length Of The Diagonal Of A Parallelogram

Parallelogram ABCD has diagonals $\overline{AC}$ and $\overline{BD}$ . AC = 12 and BD = 6 .

True, false, or undetermined: Parallelogram ABCD is a rectangle.

Possible Answers:

Undetermined

False

True

Correct answer:

False

Explanation:

One characteristic of a rectangle is that its diagonals are congruent. Since the diagonals of Parallelogram ABCD are of different lengths, it cannot be a rectangle.

Report an Error

Example Question #1 : How To Find The Length Of The Diagonal Of A Parallelogram

Parallelogram ABCD has diagonals $\overline{AC}$ and $\overline{BD}$ . AC = 12 and BD = 6 .

True, false, or undetermined: Parallelogram ABCD is a rhombus.

Possible Answers:

Undetermined

False

True

Correct answer:

Undetermined

Explanation:

One characteristic of a rhombus is that its diagonals are perpendicular; no restrictions exist as to their lengths. Whether or not the diagonals are perpendicular is not stated, so the figure may or may not be a rhombus.

Report an Error

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Parallelogram_custom_2

Find the perimeter of the parallelogram shown above.

Possible Answers:

$\small 26$

$\small 19$

$\small 48$

$\small 40$

Correct answer:

$\small 26$

Explanation:

In order to find the perimeter of this parallelogram, apply the formula:
$\small Perimeter=2(base+side)$ .

The solution is:

$\small P=2(8+5)$

$\small \small P=2(13)=26$

Report an Error

Example Question #2 : How To Find The Perimeter Of A Parallelogram

Parallelogram_custom_3

Find the perimeter of the parallelogram shown above.

Possible Answers:

$\small 112$

$\small 224$

$\small 248$

$\small 110$

Correct answer:

$\small 224$

Explanation:

To find the perimeter of this parallelogram, first find the length of the side: $\small h\times\frac{1}{3}$ .

Since, $\small h=48$ , the side must be $\small 48\div 3=16$ .

Then apply the formula:

$\small p=2(base+side)$

$\small p=2(96+16)$

$\small p=2(112)=224$

Report an Error

View Tutors

Oselen
Certified Tutor

UNIVERSITY OF BENIN, Bachelor of Science, Mechanical Engineering. University of Windsor, Master of Science, Mechanical Engine...

View Tutors

George
Certified Tutor

Pensacola State College, Bachelor in Arts, Mathematics.

View Tutors

Krittika
Certified Tutor

University of Dhaka, Master's/Graduate, Statistics. University of Waterloo, Master's/Graduate, Biostatistics.

All Intermediate Geometry Resources

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

Popular Subjects

ISEE Tutors in Los Angeles, English Tutors in Denver, Algebra Tutors in Los Angeles, GMAT Tutors in New York City, SAT Tutors in Miami, Spanish Tutors in San Francisco-Bay Area, Reading Tutors in Philadelphia, Statistics Tutors in Atlanta, Computer Science Tutors in Miami, Algebra Tutors in Houston

Popular Courses & Classes

SAT Courses & Classes in New York City, GRE Courses & Classes in Los Angeles, ACT Courses & Classes in Houston, MCAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Denver, ISEE Courses & Classes in Miami, Spanish Courses & Classes in Denver, SAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Chicago, MCAT Courses & Classes in Chicago

Popular Test Prep

ISEE Test Prep in Houston, SAT Test Prep in San Diego, MCAT Test Prep in San Diego, ACT Test Prep in Chicago, LSAT Test Prep in Denver, LSAT Test Prep in Phoenix, GRE Test Prep in Philadelphia, ACT Test Prep in Los Angeles, SAT Test Prep in Chicago, GRE Test Prep in Chicago

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 : Parallelograms

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : Parallelograms

Example Question #1 : How To Find The Length Of The Diagonal Of A Parallelogram

Example Question #3 : Parallelograms

Example Question #4 : Parallelograms

Example Question #2 : How To Find The Length Of The Diagonal Of A Parallelogram

Example Question #5 : Parallelograms

Example Question #1 : How To Find The Length Of The Diagonal Of A Parallelogram

Example Question #1 : How To Find The Length Of The Diagonal Of A Parallelogram

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Example Question #2 : How To Find The Perimeter Of A Parallelogram

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: