GMAT Math : Quadrilaterals

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

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

Example Questions

← Previous 1 2 … 6 7 8 9 10 11 12 13 14 Next →

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

Example Question #1 : Calculating An Angle In A Quadrilateral

Parallelogram

Note: Diagram is NOT drawn to scale.

Refer to the above diagram.

Any of the following facts alone would be enough to prove that $\textrm{Quad} \; ABCD$ is not a parallelogram, EXCEPT:

Possible Answers:

$m \angle D <76^{\circ}$

BC > 12

Any one of these facts alone would prove that $\textrm{Quad} \; ABCD$ is not a parallelogram.

$m \angle A = 114^{\circ}$

CD = 12

Correct answer:

BC > 12

Explanation:

Opposite sides of a parallelogram are congruent; if CD = 12 , then $CD \neq AB$ , violating this condition.

Consecutive angles of a parallelogram are supplementary; if $m \angle A = 114^{\circ}$ , then $m \angle A + m \angle B= 114 + 76 = 190$ , violating this condition.

Opposite angles of a parallelogram are congruent; if $m \angle D <76^{\circ}$ , then $m \angle D \neq m \angle B$ , violating this condition.

Adjacent sides of a parallelogram, however, may or may not be congruent, so the condition that BC > 12 would not by itself prove that the quadrilateral is not a parallelogram.

Report an Error

Example Question #2 : Calculating An Angle In A Quadrilateral

Which of the following can not be the measures of the four interior angles of a quadrilateral?

Possible Answers:

$75^{\circ },85^{\circ },95^{\circ },105^{\circ }$

All four of the other choices fit the conditions.

$80^{\circ },80^{\circ },100^{\circ },100^{\circ }$

$60^{\circ },100^{\circ },100^{\circ },100^{\circ }$

$75^{\circ },75^{\circ },75^{\circ },125^{\circ }$

Correct answer:

$75^{\circ },75^{\circ },75^{\circ },125^{\circ }$

Explanation:

The four interior angles of a quadrilateral measure a total of $360^{\circ }$ , so we test each group of numbers to see if they have this sum.

75+85+95+105 = 360

80+80+100+100 = 360

60+100+100+100 = 360

75 + 75 + 75 + 125 = 350

This last group does not have the correct sum, so it is the correct choice.

Report an Error

Example Question #1 : Calculating An Angle In A Quadrilateral

A circle can be circumscribed about each of the following figures except:

Possible Answers:

An isosceles triangle with its base one-half as long as either leg

A rectangle twice as long as it is wide

An isosceles trapezoid with one base three times as long as the other

A right scalene triangle

A rhombus with a $60^{\circ }$ angle

Correct answer:

A rhombus with a $60^{\circ }$ angle

Explanation:

A circle can be circumscribed about any triangle regardless of its sidelengths or angle measures, so we can eliminate the two triangle choices.

A circle can be circumscribed about a quadrilateral if and only if both pairs of its opposite angles are supplementary. An isosceles trapezoid has this characteristic; this can be proved by the fact that base angles are congruent, and by the Same-Side Interior Angles Statement. For a parallelogram to have this characteristic, since opposite angles are congruent also, all angles must measure $90^{\circ }$ ; the rectangle fits this description, but the rhombus does not.

Report an Error

Example Question #4 : Calculating An Angle In A Quadrilateral

Rhombus RHOM has two diagonals that intersect at point ; $\angle RHO = 80 ^{\circ }$ .

What is $m \angle RPH$ ?

Possible Answers:

$90 ^{\circ }$

$50 ^{\circ }$

$40 ^{\circ }$

$100 ^{\circ }$

$80 ^{\circ }$

Correct answer:

$90 ^{\circ }$

Explanation:

The diagonals of a rhombus always intersect at right angles, so $m \angle HPO = 90 ^{\circ }$ . The measures of the interior angles of the rhombus are irrelevant.

Report an Error

Example Question #5 : Calculating An Angle In A Quadrilateral

Quadrilateral QUAD is inscribed in circle $\bigodot$ . $m \angle A = 100 ^{\circ }$ . What is $m \angle Q$ ?

Possible Answers:

$50 ^{\circ }$

$100 ^{\circ }$

$160 ^{\circ }$

$40^{\circ }$

$80 ^{\circ }$

Correct answer:

$80 ^{\circ }$

Explanation:

Two opposite angles of a quadrilateral inscribed inside a circle are supplementary, so

$m \angle Q = 180^{\circ } - m \angle A = 180^{\circ } - 100^{\circ } = 80^{\circ }$

Report an Error

← Previous 1 2 … 6 7 8 9 10 11 12 13 14 Next →

All GMAT Math Resources

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

Popular Subjects

English Tutors in Los Angeles, Math Tutors in Boston, GMAT Tutors in Dallas Fort Worth, Statistics Tutors in Dallas Fort Worth, Computer Science Tutors in Dallas Fort Worth, ACT Tutors in Philadelphia, Statistics Tutors in San Diego, Algebra Tutors in Los Angeles, Calculus Tutors in San Francisco-Bay Area, Computer Science Tutors in San Francisco-Bay Area

Popular Courses & Classes

LSAT Courses & Classes in Houston, Spanish Courses & Classes in Washington DC, SAT Courses & Classes in Miami, SAT Courses & Classes in Chicago, SAT Courses & Classes in Washington DC, Spanish Courses & Classes in Denver, MCAT Courses & Classes in Boston, GRE Courses & Classes in Chicago, ACT Courses & Classes in Chicago, GMAT Courses & Classes in Seattle

Popular Test Prep

SAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Atlanta, SAT Test Prep in Philadelphia, SSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Houston, GMAT Test Prep in Philadelphia, ISEE Test Prep in Chicago, ACT Test Prep in Chicago, ACT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Houston

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 : Quadrilaterals

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 #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

Example Question #1 : Calculating An Angle In A Quadrilateral

Example Question #2 : Calculating An Angle In A Quadrilateral

Example Question #1 : Calculating An Angle In A Quadrilateral

Example Question #4 : Calculating An Angle In A Quadrilateral

Example Question #5 : Calculating An Angle In A Quadrilateral

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details