We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Advanced Geometry : Rhombuses

Study concepts, example questions & explanations for Advanced Geometry

Create An Account

All Advanced Geometry Resources

6 Diagnostic Tests 57 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 Next →

Example Question #111 : Quadrilaterals

Find the area of the rhombus below.

Possible Answers:

341.20

228.95

301.29

339.58

Correct answer:

228.95

Explanation:

Recall that the diagonals of the rhombus are perpendicular bisectors. From the given side and the given diagonal, we can find the length of the second diagonal by using the Pythagorean Theorem.

$\text{side}^2=(\frac{\text{diagonal 1}}{2})^2-(\frac{\text{diagonal 2}}{2})^2$

Let the given diagonal be diagonal 1, and rearrange the equation to solve for diagonal 2.

$(\frac{\text{diagonal 2}}{2})^2=\text{side}^2-(\frac{\text{diagonal 1}}{2})^2$

$(\frac{\text{diagonal 2}}{2})=\sqrt{\text{side}^2-(\frac{\text{diagonal 1}}{2})^2}$

$\text{diagonal 2}=2\sqrt{\text{side}^2-(\frac{\text{diagonal 1}}{2})^2}$

Plug in the given side and diagonal to find the length of diagonal 2.

$\text{diagonal 2}=2\sqrt{20^2-(\frac{12}{2})^2}=2\sqrt{364}$

Now, recall how to find the area of a rhombus:

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

Plug in the two diagonals to find the area.

$\text{Area of Rhombus}=\frac{(12)(2\sqrt{364})}{2}=228.95$

Make sure to round to places after the decimal.

Report an Error

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

A rhombus is $d_{2} = 10$ meters across. $d_{1} = \frac{1}{2}d_{2}$ . Find the area.

Possible Answers:

$12\textup{ m}^2$

$20\textup{ m}^2$

$5\textup{ m}^2$

$25\textup{ m}^2$

m²

Correct answer:

$25\textup{ m}^2$

Explanation:

1) Substitute $d_{2} = 10$ into the expression $d_{1} = \frac{1}{2}d_{2}$ , $d_{1} = \frac{1}{2}\cdot 10 = 5$ .

2) Substitute $d_{2} = 10$ and $d_{1} = 5$ into the rhombus area formula,

$A = \frac{1}{2}d_{1}d_{2}$

$A = \frac{1}{2}\cdot 5 \cdot 10$

$= \frac{1}{2}\cdot 50$

$= 25\textup{ m}^2$

Report an Error

Example Question #411 : Advanced Geometry

Find the area of the rhombus.

Possible Answers:

13.62

18.05

12.44

14.95

Correct answer:

13.62

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

$\text{Area}=\text{base}\times\text{height}$

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

$\sin x=\frac{\text{height}}{\text{side}}$ , where is the given angle.

$\text{height}=(\text{side})(\sin x)$

Now, plug this into the equation for the area to get the following equation:

$\text{Area}=(side)^2 \sin x$

Plug in the given side length and angle values to find the area.

$\text{Area}=(5)^2\sin 33=13.62$

Make sure to round to places after the decimal.

Report an Error

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

Find the area of the rhombus.

Possible Answers:

32.79

27.64

25.08

31.24

Correct answer:

32.79

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

$\text{Area}=\text{base}\times\text{height}$

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

$\sin x=\frac{\text{height}}{\text{side}}$ , where is the given angle.

$\text{height}=(\text{side})(\sin x)$

Now, plug this into the equation for the area to get the following equation:

$\text{Area}=(side)^2 \sin x$

Plug in the given side length and angle values to find the area.

$\text{Area}=(7)^2\sin 42=32.79$

Make sure to round to places after the decimal.

Report an Error

Example Question #121 : Quadrilaterals

Find the area of the rhombus.

Possible Answers:

38.56

45.12

39.40

31.24

Correct answer:

39.40

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

$\text{Area}=\text{base}\times\text{height}$

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

$\sin x=\frac{\text{height}}{\text{side}}$ , where is the given angle.

$\text{height}=(\text{side})(\sin x)$

Now, plug this into the equation for the area to get the following equation:

$\text{Area}=(side)^2 \sin x$

Plug in the given side length and angle values to find the area.

$\text{Area}=(8)^2\sin 38=39.40$

Make sure to round to places after the decimal.

Report an Error

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

Find the area of the rhombus.

Possible Answers:

39.78

31.93

40.51

32.95

Correct answer:

32.95

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

$\text{Area}=\text{base}\times\text{height}$

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

$\sin x=\frac{\text{height}}{\text{side}}$ , where is the given angle.

$\text{height}=(\text{side})(\sin x)$

Now, plug this into the equation for the area to get the following equation:

$\text{Area}=(side)^2 \sin x$

Plug in the given side length and angle values to find the area.

$\text{Area}=(9)^2\sin 24=32.95$

Make sure to round to places after the decimal.

Report an Error

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

Find the area of the rhombus.

Possible Answers:

52.19

63.21

Correct answer:

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

$\text{Area}=\text{base}\times\text{height}$

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

$\sin x=\frac{\text{height}}{\text{side}}$ , where is the given angle.

$\text{height}=(\text{side})(\sin x)$

Now, plug this into the equation for the area to get the following equation:

$\text{Area}=(side)^2 \sin x$

Plug in the given side length and angle values to find the area.

$\text{Area}=(10)^2\sin 30=50$

Report an Error

Example Question #121 : Quadrilaterals

Find the area of the rhombus.

Possible Answers:

227.61

205.41

213.49

217.10

Correct answer:

217.10

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

$\text{Area}=\text{base}\times\text{height}$

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

$\sin x=\frac{\text{height}}{\text{side}}$ , where is the given angle.

$\text{height}=(\text{side})(\sin x)$

Now, plug this into the equation for the area to get the following equation:

$\text{Area}=(side)^2 \sin x$

Plug in the given side length and angle values to find the area.

$\text{Area}=(16)^2\sin 58=217.10$

Make sure to round to places after the decimal.

Report an Error

Example Question #122 : Quadrilaterals

Find the area of the rhombus.

Possible Answers:

551.68

500.24

573.81

495.81

Correct answer:

573.81

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

$\text{Area}=\text{base}\times\text{height}$

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

$\sin x=\frac{\text{height}}{\text{side}}$ , where is the given angle.

$\text{height}=(\text{side})(\sin x)$

Now, plug this into the equation for the area to get the following equation:

$\text{Area}=(side)^2 \sin x$

Plug in the given side length and angle values to find the area.

$\text{Area}=(24)^2\sin 95=573.81$

Make sure to round to places after the decimal.

Report an Error

Example Question #421 : Advanced Geometry

Find the area of the rhombus.

Possible Answers:

3.88

3.49

5.37

2.91

Correct answer:

3.88

Explanation:

Recall that one of the ways to find the area of a rhombus is with the following formula:

$\text{Area}=\text{base}\times\text{height}$

Now, since all four sides in the rhombus are the same, we know from the given side value what the length of the base will be. In order to find the length of the height, we will need to use sine.

$\sin x=\frac{\text{height}}{\text{side}}$ , where is the given angle.

$\text{height}=(\text{side})(\sin x)$

Now, plug this into the equation for the area to get the following equation:

$\text{Area}=(side)^2 \sin x$

Plug in the given side length and angle values to find the area.

$\text{Area}=(2)^2\sin 104=3.88$

Make sure to round to places after the decimal.

Report an Error

← Previous 1 2 3 4 5 6 7 Next →

View Tutors

Euna
Certified Tutor

Ewha Womens Univ, Bachelor, Ceramic Arts. Lynn University, Bachelor in Arts, Animation and Special Effects.

View Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

View Tutors

Jascinth
Certified Tutor

University of Phoenix-Online Campus, Bachelor in Business Administration, Business Administration and Management. University ...

All Advanced Geometry Resources

6 Diagnostic Tests 57 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in New York City, Computer Science Tutors in San Francisco-Bay Area, English Tutors in Los Angeles, SSAT Tutors in Dallas Fort Worth, LSAT Tutors in Phoenix, ACT Tutors in Houston, Statistics Tutors in Chicago, Algebra Tutors in San Francisco-Bay Area, Reading Tutors in Houston, ISEE Tutors in San Diego

Popular Courses & Classes

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

Popular Test Prep

SSAT Test Prep in Phoenix, GRE Test Prep in Seattle, MCAT Test Prep in Denver, SAT Test Prep in Denver, MCAT Test Prep in Houston, GRE Test Prep in Denver, ISEE Test Prep in Chicago, LSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Dallas Fort Worth, SAT Test Prep in New York City

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

Advanced Geometry : Rhombuses

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #111 : Quadrilaterals

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

Example Question #411 : Advanced Geometry

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

Example Question #121 : Quadrilaterals

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

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

Example Question #121 : Quadrilaterals

Example Question #122 : Quadrilaterals

Example Question #421 : Advanced Geometry

All Advanced Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: