We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : How to find the perimeter of a rhombus

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

← Previous 1 2 3 4 Next →

Example Question #31 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus that has an area of 150 and a diagonal of .

Possible Answers:

Correct answer:

Explanation:

Recall the following properties of a rhombus, as shown by the figure above: The diagonals of a rhombus are perpendicular and they bisect each other. Thus, if we know the lengths of the diagonals, we can use the Pythagorean theorem to find the length of a side of the rhombus.

Recall how to find the area of a rhombus:

$\text{Area}=\frac{(\text{diagonal 1})(\text{diagonal 2})}{2}$

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(\text{Area})}{\text{diagonal 1}}$

Plug in the given values to find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(150)}{15}=20$

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

$\text{Half diagonal 1}=\frac{15}{2}=7.5$

$\text{Half diagonal 2}=\frac{20}{2}=10$

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

$\text{Side of Rhombus}=\sqrt{7.5^2+100^2}=\sqrt{156.25}$

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

$\text{Perimeter of rhombus}=4\sqrt{156.25}=50$

Report an Error

Example Question #32 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has an area of and a diagonal of .

Possible Answers:

39.67

32.81

20.36

28.84

Correct answer:

28.84

Explanation:

Recall how to find the area of a rhombus:

$\text{Area}=\frac{(\text{diagonal 1})(\text{diagonal 2})}{2}$

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(\text{Area})}{\text{diagonal 1}}$

Plug in the given values to find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(48)}{8}=12$

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

$\text{Half diagonal 1}=\frac{8}{2}=4$

$\text{Half diagonal 2}=\frac{12}{2}=6$

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

$\text{Side of Rhombus}=\sqrt{4^2+6^2}=\sqrt{52}$

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

$\text{Perimeter of rhombus}=4\sqrt{52}=28.84$

Make sure to round to places after the decimal.

Report an Error

Example Question #41 : Quadrilaterals

Find the perimeter of a rhombus if it has an area of 152 and a diagonal of .

Possible Answers:

45.26

49.68

52.33

47.01

Correct answer:

49.68

Explanation:

Recall how to find the area of a rhombus:

$\text{Area}=\frac{(\text{diagonal 1})(\text{diagonal 2})}{2}$

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(\text{Area})}{\text{diagonal 1}}$

Plug in the given values to find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(152)}{16}=19$

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

$\text{Half diagonal 1}=\frac{16}{2}=8$

$\text{Half diagonal 2}=\frac{19}{2}=9.5$

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

$\text{Side of Rhombus}=\sqrt{8^2+9.5^2}=\sqrt{154.25}$

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

$\text{Perimeter of rhombus}=4\sqrt{154.25}=49.68$

Make sure to round to places after the decimal.

Report an Error

Example Question #34 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has an area of 187 and a diagonal of .

Possible Answers:

65.29

59.37

50.44

55.61

Correct answer:

55.61

Explanation:

Recall how to find the area of a rhombus:

$\text{Area}=\frac{(\text{diagonal 1})(\text{diagonal 2})}{2}$

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(\text{Area})}{\text{diagonal 1}}$

Plug in the given values to find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(187)}{17}=22$

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

$\text{Half diagonal 1}=\frac{17}{2}=8.5$

$\text{Half diagonal 2}=\frac{22}{2}=11$

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

$\text{Side of Rhombus}=\sqrt{8.5^2+11^2}=\sqrt{193.25}$

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

$\text{Perimeter of rhombus}=4\sqrt{193.25}=55.61$

Make sure to round to places after the decimal.

Report an Error

Example Question #35 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has an area of 228 and a diagonal of .

Possible Answers:

61.22

65.03

71.85

69.81

Correct answer:

61.22

Explanation:

Recall how to find the area of a rhombus:

$\text{Area}=\frac{(\text{diagonal 1})(\text{diagonal 2})}{2}$

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(\text{Area})}{\text{diagonal 1}}$

Plug in the given values to find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(228)}{19}=24$

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

$\text{Half diagonal 1}=\frac{19}{2}=9.5$

$\text{Half diagonal 2}=\frac{24}{2}=12$

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

$\text{Side of Rhombus}=\sqrt{9.5^2+12^2}=\sqrt{234.25}$

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

$\text{Perimeter of rhombus}=4\sqrt{234.25}=61.22$

Make sure to round to places after the decimal.

Report an Error

Example Question #36 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has an area of and a diagonal of .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a rhombus:

$\text{Area}=\frac{(\text{diagonal 1})(\text{diagonal 2})}{2}$

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(\text{Area})}{\text{diagonal 1}}$

Plug in the given values to find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(96)}{12}=16$

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

$\text{Half diagonal 1}=\frac{12}{2}=6$

$\text{Half diagonal 2}=\frac{16}{2}=8$

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

$\text{Side of Rhombus}=\sqrt{6^2+8^2}=\sqrt{100}=10$

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

$\text{Perimeter of rhombus}=4(10)=40$

Report an Error

Example Question #37 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus that has an area of 210 and a diagonal of .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a rhombus:

$\text{Area}=\frac{(\text{diagonal 1})(\text{diagonal 2})}{2}$

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(\text{Area})}{\text{diagonal 1}}$

Plug in the given values to find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(210)}{20}=21$

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

$\text{Half diagonal 1}=\frac{20}{2}=10$

$\text{Half diagonal 2}=\frac{21}{2}=10.5$

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

$\text{Side of Rhombus}=\sqrt{10^2+10.5^2}=\sqrt{210.25}$

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

$\text{Perimeter of rhombus}=4\sqrt{210.25}=58$

Report an Error

Example Question #38 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has an area of 1200 and a diagonal length of .

Possible Answers:

144.22

152.36

188.03

174.22

Correct answer:

144.22

Explanation:

Recall how to find the area of a rhombus:

$\text{Area}=\frac{(\text{diagonal 1})(\text{diagonal 2})}{2}$

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(\text{Area})}{\text{diagonal 1}}$

Plug in the given values to find the length of the second diagonal.

$\text{diagonal 2}=\frac{2(1200)}{40}=60$

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

$\text{Half diagonal 1}=\frac{40}{2}=20$

$\text{Half diagonal 2}=\frac{60}{2}=30$

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

$\text{Side of Rhombus}=\sqrt{20^2+30^2}=\sqrt{1300}$

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

$\text{Perimeter of rhombus}=4\sqrt{1300}=144.22$

Make sure to round to places after the decimal.

Report an Error

Example Question #39 : How To Find The Perimeter Of A Rhombus

Given Rhombus ABCD and diagonal $\overline{ BD}$ .

$m \angle ABD = 25 ^{\circ }$

$m \angle BCD = ?$

Possible Answers:

$105^{\circ }$

$155^{\circ }$

$\textup{The question cannot be answered from the information given}$

$110^{\circ }$

$130 ^{\circ }$

Correct answer:

$130 ^{\circ }$

Explanation:

The rhombus referenced is below:

Rhombus

A diagonal of a rhombus bisects the angles of the rhombus at its endpoints. Therefore, since $m \angle ABD = 25 ^{\circ }$ , it follows that $m \angle DBC = 25 ^{\circ }$ as well. By angle addition,

$m \angle ABC = m \angle ABD + m \angle DBC = 25^{\circ }+ 25^{\circ } = 50^{\circ }$ .

As consecutive angles of a rhombus (and, consequently, of a parallelogram), $\angle ABC$ and $\angle BDC$ are supplementary - that is, their measures total $180^{\circ }$ . Therefore,

$m \angle ABC + m \angle BCD = 180^{\circ }$

$50 ^{\circ } + m \angle BCD = 180^{\circ }$

$50 ^{\circ } + m \angle BCD - 50 ^{\circ } = 180^{\circ } - 50 ^{\circ }$

$m \angle BCD = 130 ^{\circ }$

Report an Error

← Previous 1 2 3 4 Next →

View Tutors

Samuel
Certified Tutor

Oregon State University, Bachelor in Arts, Political Science and Government.

View Tutors

Paul
Certified Tutor

Aston University, Bachelor of Science, Theoretical and Mathematical Physics. Oglethorpe University, Master of Arts, Accounting.

View Tutors

Jean Bosco
Certified Tutor

Carnegie Mellon University, Master of Electrical Engineering, Electrical Engineering Technology. University of Massachusetts ...

All Intermediate Geometry Resources

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

Popular Subjects

Algebra Tutors in San Francisco-Bay Area, Chemistry Tutors in San Francisco-Bay Area, Computer Science Tutors in Houston, Computer Science Tutors in Phoenix, Math Tutors in Boston, English Tutors in San Francisco-Bay Area, Algebra Tutors in Miami, Reading Tutors in Atlanta, Reading Tutors in Miami, Chemistry Tutors in Denver

Popular Courses & Classes

MCAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Phoenix, GMAT Courses & Classes in Miami, SSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Houston, ISEE Courses & Classes in Los Angeles, LSAT Courses & Classes in Washington DC, MCAT Courses & Classes in Washington DC, LSAT Courses & Classes in Miami, GRE Courses & Classes in San Diego

Popular Test Prep

SSAT Test Prep in Philadelphia, SSAT Test Prep in Atlanta, ISEE Test Prep in San Diego, MCAT Test Prep in Denver, SAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Atlanta, GRE Test Prep in San Diego, GRE Test Prep in Houston, LSAT Test Prep in Houston, ISEE 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 : How to find the perimeter of a rhombus

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #31 : How To Find The Perimeter Of A Rhombus

Example Question #32 : How To Find The Perimeter Of A Rhombus

Example Question #41 : Quadrilaterals

Example Question #34 : How To Find The Perimeter Of A Rhombus

Example Question #35 : How To Find The Perimeter Of A Rhombus

Example Question #36 : How To Find The Perimeter Of A Rhombus

Example Question #37 : How To Find The Perimeter Of A Rhombus

Example Question #38 : How To Find The Perimeter Of A Rhombus

Example Question #39 : How To Find The Perimeter Of A Rhombus

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: