GMAT Math : Calculating the length of the side of a quadrilateral

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Calculating The Length Of The Side Of A Quadrilateral

The area of a trapezoid is 1,600 square centimeters. Its height is 24 centimeters, and one base is one decimeter longer than the other. What is the length of the longer base?

Possible Answers:

$716 \frac{2}{3}\textrm{ cm}$

$616 \frac{2}{3}\textrm{ cm}$

$71 \frac{2}{3}\textrm{ cm}$

$61 \frac{2}{3}\textrm{ cm}$

$66 \frac{2}{3}\textrm{ cm}$

Correct answer:

$71 \frac{2}{3}\textrm{ cm}$

Explanation:

Let be the longer base. Then, since this is ten centimeters (= 1 decimeter) longer than the shorter, the shorter base has length B - 10 . Substitute A = 1,600, b = B - 10, h = 24 in the formula for the area of a trapezoid, and solve for :

$\frac{1}{2} (B + b)h = A$

$\frac{1}{2} (B + B - 10) \cdot 24= 1,600$

12 (2B - 10) = 1,600

24B - 120 = 1,600

24B = 1,720

$24B \div 24 = 1,720 \div 24$

$B = 71 \frac{2}{3}$ centimeters

Report an Error

Example Question #1 : Calculating The Length Of The Side Of A Quadrilateral

The area of a trapezoid is 6,000 square inches. Its height is twice the length of its ionger base, which is three times the length of its shorter base. What is the height of the trapezoid?

Possible Answers:

$30 \sqrt{5 } \textrm{ in}$

$60 \sqrt{5 } \textrm{ in}$

$60 \textrm{ in}$

$30 \textrm{ in}$

$10 \sqrt{5 } \textrm{ in}$

Correct answer:

$60 \sqrt{5 } \textrm{ in}$

Explanation:

Let be the length of the shorter base. Then is the length of its longer base, and 2 (3b)= 6b is the height. Substitute B = 3b, h = 6b , A = 6,666 in the area formula:

$\frac{1}{2} ( B + b) h = A$

$\frac{1}{2} ( 3b + b) \cdot 6b= 6,000$

$\frac{1}{2} \cdot 4b \cdot 6b= 6,000$

$12b^{2}= 6,000$

$12b^{2} \div 12 = 6,000 \div 12$

$b^{2} = 500$

$b = \sqrt{500} = \sqrt{100}\cdot \sqrt{5 } =10 \sqrt{5 }$

The height is six times this, or $h = 6 \cdot 10 \sqrt{5 } = 60 \sqrt{5 }$ inches.

Report an Error

Example Question #1 : Calculating The Length Of The Side Of A Quadrilateral

A trapezoid has bases of length one mile and 4,000 feet and height one-half mile. What is the length of its midsegment?

Possible Answers:

$3,320\textrm{ ft}$

$4,500 \textrm{ ft}$

$3,960\textrm{ ft}$

$2,640\textrm{ ft}$

$4,640\textrm{ ft}$

Correct answer:

$4,640\textrm{ ft}$

Explanation:

The length of the midsegment of a trapezoid is the mean of the lengths of its bases; the height is irrelevant. The bases are of length 4,000 feet and 5,280 feet; their mean is

$\frac{1}{2} \left ( 5,280 + 4,000 \right ) = 4,640$ feet, the length of the midsegment.

Report an Error

Example Question #4 : Calculating The Length Of The Side Of A Quadrilateral

A given trapezoid has an area of $2500\:cm^2$ , a longer base of length $70\:cm$ , and a height of $50\:cm$ . What is the length of the shorter base?

Possible Answers:

$20\:cm$

$25\:cm$

$40\:cm$

$30\:cm$

$50\:cm$

Correct answer:

$30\:cm$

Explanation:

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}(B+b)h$

2A=(B+b)h

$\frac{2A}{h}=B+b$

$\frac{2A}{h}-B=b$

Plugging in our values for , , and :

$\frac{2(2500)}{50}-70=b$

30=b

Report an Error

Example Question #5 : Calculating The Length Of The Side Of A Quadrilateral

A given trapezoid has an area of $1000\:cm^2$ , a longer base of length $60\:cm$ , and a height of $20\:cm$ . What is the length of the shorter base?

Possible Answers:

$45\:cm$

$40\:cm$

$50\:cm$

$20\:cm$

$25\:cm$

Correct answer:

$40\:cm$

Explanation:

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}(B+b)h$

2A=(B+b)h

$\frac{2A}{h}=B+b$

$\frac{2A}{h}-B=b$

Plugging in our values for , , and :

$\frac{2(1000)}{20}-60=b$

40=b

Report an Error

Example Question #6 : Calculating The Length Of The Side Of A Quadrilateral

A given trapezoid has an area of $4000\:cm^2$ , a longer base of length $120\:cm$ , and a height of $40\:cm$ . What is the length of the shorter base?

Possible Answers:

$95\:cm$

$80\:cm$

$110\:cm$

$60\:cm$

$100\:cm$

Correct answer:

$80\:cm$

Explanation:

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}(B+b)h$

2A=(B+b)h

$\frac{2A}{h}=B+b$

$\frac{2A}{h}-B=b$

Plugging in our values for , , and :

$\frac{2(4000)}{40}-120=b$

$\frac{8000}{40}-120=b$

200-120=b

80=b

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GRE Tutors in Denver, LSAT Tutors in Atlanta, GRE Tutors in Atlanta, MCAT Tutors in San Diego, Spanish Tutors in San Francisco-Bay Area, SAT Tutors in Dallas Fort Worth, English Tutors in Boston, LSAT Tutors in Miami, Chemistry Tutors in San Diego, ACT Tutors in Phoenix

Popular Courses & Classes

SSAT Courses & Classes in San Diego, GMAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Los Angeles, GRE Courses & Classes in Houston, SSAT Courses & Classes in Atlanta, ISEE Courses & Classes in San Diego, ACT Courses & Classes in Denver, GMAT Courses & Classes in Boston, SAT Courses & Classes in Philadelphia, LSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ISEE Test Prep in San Diego, SSAT Test Prep in Miami, MCAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Boston, MCAT Test Prep in Phoenix, GMAT Test Prep in Boston, MCAT Test Prep in Washington DC, SSAT Test Prep in Los Angeles, SSAT Test Prep in Houston, GRE Test Prep in Washington DC

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)

Email address:
Your name:
Feedback:

GMAT Math : Calculating the length of the side of a quadrilateral

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating The Length Of The Side Of A Quadrilateral

Example Question #1 : Calculating The Length Of The Side Of A Quadrilateral

Example Question #1 : Calculating The Length Of The Side Of A Quadrilateral

Example Question #4 : Calculating The Length Of The Side Of A Quadrilateral

Example Question #5 : Calculating The Length Of The Side Of A Quadrilateral

Example Question #6 : Calculating The Length Of The Side Of A Quadrilateral

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details