GMAT Math : Calculating the area of a quadrilateral

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

Example Question #1 : Other Quadrilaterals

What is the area of a trapezoid with a height of 7, a base of 5, and another base of 13?

Possible Answers:

$\dpi{100} \small 39$

$\dpi{100} \small 63$

$\dpi{100} \small 43$

$\dpi{100} \small 51$

$\dpi{100} \small 29$

Correct answer:

$\dpi{100} \small 63$

Explanation:

$area = \frac{(b_{1}+ b_{2}\cdot h)}{2} = \frac{(5 + 13)\cdot 7}{2} = \frac{18\cdot 7}{2} = \frac{126}{2} = 63$

Report an Error

Example Question #2 : Other Quadrilaterals

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

Possible Answers:

A triangle with sides 30, 40, 50.

Each of the figures given in the other choices can have a circle circumscribed about it.

A $30^{\circ } -60 ^{\circ }-90^{\circ }$ triangle

A regular pentagon

A regular hexagon

Correct answer:

Each of the figures given in the other choices can have a circle circumscribed about it.

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 any regular polygon, so we can eliminate those two choices as well.

The correct choice is that each figure can have a circle circumscribed about it.

Report an Error

Example Question #3 : Other Quadrilaterals

What is the area of a quadrilateral on the coordinate plane with vertices (0.0),(8.0),(3,4),(11,4) ?

Possible Answers:

Correct answer:

Explanation:

As can be seen from this diagram, this is a parallelogram with base 8 and height 4:

Parallelogram

The area of this parallelogram is the product of its base and its height:

$A = bh = 8 \cdot 4 = 32$

Report an Error

Example Question #4 : Other Quadrilaterals

What is the area of a quadrilateral on the coordinate plane with vertices (0,0), (0,10),(8,2), (8,7) ?

Possible Answers:

120

Correct answer:

Explanation:

As can be seen in this diagram, this is a trapezoid with bases 10 and 5 and height 8.

Trapezoid

Setting B = 10, b = 5, h = 8 in the following formula, we can calculate the area of the trapezoid:

$A = \frac{1}{2} (B + b) h = \frac{1}{2} \cdot (10 + 5)\cdot 8 = 60$

Report an Error

Example Question #5 : Calculating The Area Of A Quadrilateral

Quad

Note: Figure NOT drawn to scale

What is the area of Quadrilateral QUAD , above?

Possible Answers:

$38 \frac{1}{2}$

$42 \frac{1}{2}$

Correct answer:

Explanation:

Quadrilateral QUAD is a composite of two right triangles, $\Delta ADU$ and $\Delta DUQ$ , so we find the area of each and add the areas. First, we need to find and , since the area of a right triangle is half the product of the lengths of its legs.

By the Pythagorean Theorem:

$\left (AD \right )^{2} +\left ( AU\right ) ^{2} =\left ( DU\right ) ^{2}$

$\left (AD \right )^{2} +4 ^{2} =5 ^{2}$

$\left (AD \right )^{2} +16 =25$

$\left (AD \right )^{2} +16 -16 =25 -16$

$\left (AD \right )^{2} =9$

AD = 3

Also by the Pythagorean Theorem:

$\left ( QU\right ) ^{2} + \left ( DU\right ) ^{2}=\left ( DQ\right ) ^{2}$

$\left ( QU\right ) ^{2} + 5^{2}=13^{2}$

$\left ( QU\right ) ^{2} + 25 =169$

$\left ( QU\right ) ^{2} + 25 -25=169 -25$

$\left ( QU\right ) ^{2} =144$

QU = 12

The area of $\Delta ADU$ is $\frac{1}{2} \cdot AD \cdot AU = \frac{1}{2} \cdot 3 \cdot 4 = 6$ .

The area of $\Delta DUQ$ is $\frac{1}{2} \cdot DU \cdot QU = \frac{1}{2} \cdot 5 \cdot 12 = 30$ .

Add the areas to get 6 + 30 = 36 , the area of Quadrilateral QUAD .

Report an Error

Example Question #3 : Calculating The Area Of A Quadrilateral

What is the area of the quadrilateral on the coordinate plane with vertices (0,0), (9,0), (4, 7), (7,7) ?

Possible Answers:

Correct answer:

Explanation:

The quadrilateral formed is a trapezoid with two horizontal bases. One base connects (0,0) and (9,0) and therefore has length 9 - 0 = 9 ; the other connects (4,7) and (7,7) and has length 7-4 = 3 . The height is the vertical distance between the two bases, which is the difference of the coorindates: 7 - 0 = 7 . Therefore, the area of the trapezoid is

$A = \frac{1}{2} (B + b ) h = \frac{1}{2} \cdot (9+3 ) \cdot 7 = 42$

Report an Error

Example Question #6 : Calculating The Area Of A Quadrilateral

What is the area of the quadrilateral on the coordinate plane with vertices (-2, -1), (8, -1), (-1, 5), (5,5) .

Possible Answers:

Correct answer:

Explanation:

The quadrilateral is a trapezoid with horizontal bases; one connects (-2, -1) and (8, -1) and has length 8 - (-2) = 10 , and the other connects (-1, 5) and (5,5) and has length 5 - (-1) = 6 . The height is the vertical distance between the bases, which is the difference of the -coordinates; this is . Substitute B = 10, b = 6, h = 6 in the formula for the area of a trapezoid:

$A = \frac{1}{2} (B + b)h = \frac{1}{2}\cdot (10+6) \cdot 6 = 48$

Report an Error

Example Question #5 : Other Quadrilaterals

What is the area of the quadrilateral on the coordinate plane with vertices (-4, 8) , (-4, 15), (-9, 6), (-9, 13) ?

Possible Answers:

Correct answer:

Explanation:

The quadrilateral is a parallelogram with two vertical bases, each with length 15-8 = 13-6 = 7 . Its height is the distance between the bases, which is the difference of the -coordinates: -4 - (-9) = 5 . The area of the parallelogram is the product of its base and its height:

$7 \times 5 = 35$

Report an Error

Example Question #201 : Geometry

Parallelogram1

Give the area of the above parallelogram if BC = 16 .

Possible Answers:

$128\sqrt{2}$

$64\sqrt{3}$

128

$64\sqrt{2}$

Correct answer:

128

Explanation:

Multiply height by base to get the area.

By the 45-45-90 Theorem,

$BD=CD = BC \div \sqrt{2} = \frac{16}{\sqrt{2}} = \frac{16\cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{16 \sqrt{2}}{2} = 8 \sqrt{2}$ .

Since the product of the height and the base of a parallelogram is its area,

$A = BD \cdot CD$

$= 8 \sqrt{2} \cdot 8 \sqrt{2}$

$= 8\cdot 8 \cdot \sqrt{2} \cdot \sqrt{2}$

$= 8\cdot 8 \cdot 2$

= 128

Report an Error

Example Question #1 : Calculating The Area Of A Quadrilateral

Parallelogram2

Give the area of the above parallelogram if BC = 10 .

Possible Answers:

$25\sqrt{2}$

$50\sqrt{2}$

$25\sqrt{3}$

Correct answer:

$25\sqrt{3}$

Explanation:

Multiply height by base to get the area.

By the 30-60-90 Theorem:

$CD= \frac{BC}{2} = \frac{10}{2}} = 5$ .

$BD =CD \sqrt{3} = 5\sqrt{3}$

The area is therefore

$BD \cdot CD = 5\sqrt{3} \cdot 5= 25\sqrt{3}$

Report an Error

All GMAT Math Resources

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

Popular Subjects

SSAT Tutors in Washington DC, Algebra Tutors in Phoenix, Computer Science Tutors in Philadelphia, Spanish Tutors in Dallas Fort Worth, LSAT Tutors in San Diego, Computer Science Tutors in Houston, SAT Tutors in San Diego, Computer Science Tutors in New York City, SAT Tutors in Washington DC, Computer Science Tutors in Phoenix

Popular Courses & Classes

GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Chicago, GMAT Courses & Classes in Seattle, Spanish Courses & Classes in Denver, LSAT Courses & Classes in Atlanta, Spanish Courses & Classes in Boston, ISEE Courses & Classes in Boston, MCAT Courses & Classes in New York City, ACT Courses & Classes in Miami

Popular Test Prep

SSAT Test Prep in Phoenix, GMAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Atlanta, SSAT Test Prep in Los Angeles, GMAT Test Prep in Chicago, ACT Test Prep in Dallas Fort Worth, SAT Test Prep in Boston, MCAT Test Prep in Atlanta, LSAT Test Prep in Boston, MCAT 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)

Email address:
Your name:
Feedback:

GMAT Math : Calculating the area of a quadrilateral

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Other Quadrilaterals

Example Question #2 : Other Quadrilaterals

Example Question #3 : Other Quadrilaterals

Example Question #4 : Other Quadrilaterals

Example Question #5 : Calculating The Area Of A Quadrilateral

Example Question #3 : Calculating The Area Of A Quadrilateral

Example Question #6 : Calculating The Area Of A Quadrilateral

Example Question #5 : Other Quadrilaterals

Example Question #201 : Geometry

Example Question #1 : Calculating The Area Of A Quadrilateral

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details