GMAT Math : Geometry

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 #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 #3 : Calculating The Area Of A Quadrilateral

Parallelogram2

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

Possible Answers:

$50\sqrt{2}$

$25\sqrt{3}$

$25\sqrt{2}$

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

Example Question #91 : Quadrilaterals

Parallelogram2

Give the area of the above parallelogram if BC = 30 .

Possible Answers:

$225\sqrt{3}$

$75\sqrt{2}$

$225\sqrt{2}$

$75\sqrt{3}$

225

Correct answer:

$225\sqrt{3}$

Explanation:

Multiply height by base to get the area.

By the 30-60-90 Theorem:

$BD= \frac{BC}{2} = \frac{30}{2}} = 15$ .

$CD =BD \sqrt{3} = 15\sqrt{3}$

The area is therefore

$BD \cdot CD =15 \cdot 15\sqrt{3} = 225\sqrt{3}$

Report an Error

Example Question #92 : Quadrilaterals

Triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the area of Quadrilateral ABCD .

Possible Answers:

154

144

160

150

The correct answer is not among the other choices.

Correct answer:

144

Explanation:

Apply the Pythagorean Theorem twice here.

$BD = \sqrt{6^{2}+ 8^{2}} = \sqrt{36+64 } = \sqrt{100}= 10$

$BC = \sqrt{26^{2}-10^{2}} = \sqrt{676-100} = \sqrt{576} = 24$

The quadrilateral is a composite of two right triangles, each of whose area is half the product of its legs:

Area of $\Delta ABD$ : $\frac{1}{2} \times 6 \times 8 = 24$

Area of $\Delta BCD$ : $\frac{1}{2} \times 10 \times 24= 120$

Add:

A = 24 + 120 = 144

Report an Error

Example Question #12 : How To Find The Area Of A Rhombus

Rhombus_1

The above figure shows a rhombus RHOM . Give its area.

Possible Answers:

$40\sqrt{61}$

$40 \sqrt{11}$

120

Correct answer:

$40 \sqrt{11}$

Explanation:

Construct the other diagonal of the rhombus, which, along with the first one, form a pair of mutual perpendicular bisectors.

Rhombus_1

By the Pythagorean Theorem,

$n = \sqrt{12^{2}- 10^{2}} =\sqrt{144- 100} = \sqrt{44}= \sqrt{4}\cdot \sqrt{11} = 2 \sqrt{11}$

The rhombus can be seen as the composite of four congruent right triangles, each with legs 10 and $2 \sqrt{11}$ , so the area of the rhombus is

$A = 4 \cdot \frac{1}{2}\cdot 10 \cdot 2\sqrt{11} =40 \sqrt{11}$ .

Report an Error

Example Question #391 : Advanced Geometry

Rhombus ABCD has perimeter 48; AC = 12 . What is the area of Rhombus ABCD ?

Possible Answers:

$72 \sqrt{2}$

$72 \sqrt{3}$

144

$144 \sqrt{3}$

Correct answer:

$72 \sqrt{3}$

Explanation:

Each side of a rhombus is congruent, so if it has perimeter 48, it has sidelength 12. Also, the diagonals of a rhombus are each other's perpendicular bisectors, so if they are both constructed, and their point of intersection is called , then AM = 6 . The following figure is formed by the rhombus and its diagonals.

Untitled

$\bigtriangleup AMB$ is a right triangle with its short leg half the length of its hypotenuse, so it is a 30-60-90 triangle, and its long leg measures $6\sqrt{3}$ by the 30-60-90 Theorem. Therefore, $BD = 12\sqrt{3}$ . The area of a rhombus is half the product of the lengths of its diagonals:

$\frac{1}{2} \times 12 \times 12 \sqrt{3} = 72 \sqrt{3}$

Report an Error

Example Question #14 : Other Quadrilaterals

Trapezoid 2

Note: figure NOT drawn to scale.

Give the area of the above trapezoid.

Possible Answers:

$5 \cdot 2^{2x }$

$5 \cdot 2^{2x-1 }$

$3 \cdot 2^{2x }$

$2^{2x+1 }$

$3 \cdot 2^{2x-1 }$

Correct answer:

$3 \cdot 2^{2x-1 }$

Explanation:

The area of a trapezoid with height and bases of length and is

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

Setting $h= b = 2^{x}, B = 2^{x+1}$ :

$A = \frac{1}{2} ( 2^{x+1} + 2^{x}) \cdot 2^{x}$

$= \frac{1}{2} ( 2 \cdot 2^{x } + 2^{x}) \cdot 2^{x}$

$= 2^{-1}\cdot 2^{x} \cdot ( 2 \cdot 2^{x } + 2^{x})$

$= 2^{x-1} \cdot ( 2 \cdot 2^{x } + 2^{x})$

$= 2^{x-1} \cdot 3 \cdot 2^{x }$

$= 3 \cdot 2^{x+x-1 }$

$= 3 \cdot 2^{2x-1 }$

Report an Error

Example Question #15 : Other Quadrilaterals

Trapezoid 1

Note: figure NOT drawn to scale.

Give the area of the above trapezoid.

Possible Answers:

$2^{2x+2}$

$2^{2x+1}$

$2^{x^{2}+1}$

$2^{2x }$

$2^{x^{2}+x}$

Correct answer:

$2^{2x+1}$

Explanation:

The area of a trapezoid with height and bases of length and is

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

Setting $h= b = 2^{x}, B = 3 \cdot 2^{x}$ :

$A = \frac{1}{2} (3 \cdot 2^{x} + 2^{x}) \cdot 2^{x}$

$= \frac{1}{2} \cdot 4 \cdot 2^{x} \cdot 2^{x}$

$= 2 \cdot 2^{x} \cdot 2^{x}$

$= 2^{1} \cdot 2^{x} \cdot 2^{x}$

$= 2^{1+x+x}$

$= 2^{2x+1}$

Report an Error

Example Question #16 : Other Quadrilaterals

Rhombus

Note: figure NOT drawn to scale.

The above figure depicts a rhombus, RHOM .

$HM = 2^{X}$

RO = 2 (HM)

Give the area of Rhombus RHOM .

Possible Answers:

$2^{x}$

$2^{2x-1}$

$2^{2x}$

$2^{3x}$

$2^{2x+1}$

Correct answer:

$2^{2x}$

Explanation:

The area of a rhombus is half the product of the lengths of its diagonals, so

$A = \frac{1}{2} \cdot RO \cdot HM$

$= \frac{1}{2} \cdot 2 (HM)\cdot HM$

$= HM \cdot HM$

$= 2 ^{x} \cdot 2 ^{x}$

$= 2^{x+x}$

$= 2^{2x}$

Report an Error

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

While walking with some friends on campus, you come across an open grassy rectangular area. You shout "Pythagoras!" and run across the rectangular area from one corner to another. If the rectangle measures meters by meters, what distance did you cover?

Possible Answers:

65 m

70 m

45 m

85 m

50 m

Correct answer:

65 m

Explanation:

This problem can be solved in a variety of ways, however you do it, it may be worth eliminating any options shorter than either side of the quad. The diagonal distance is the hypotenuse of a triangle, so it must be longer than 25 or 60 meters.

Then, we can either find our hypotenuse via Pythagorean Theorem, or our knowledge of Pythagorean Triples.

Using Pythagorean Theorem:

c^2=a^2+b^2

$c=\sqrt{25^2+60^2}=\sqrt{4225}=65$

So 65 meters.

Alternatively, recognize the triangle as a 5x/12x/13x triangle

5x=25

12x=60

13x=?

x=5 so 13x=65

Report an Error

All GMAT Math Resources

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

Popular Subjects

LSAT Tutors in Houston, GMAT Tutors in San Francisco-Bay Area, Computer Science Tutors in Atlanta, Computer Science Tutors in San Diego, Biology Tutors in San Diego, SAT Tutors in Denver, GMAT Tutors in Boston, French Tutors in Miami, MCAT Tutors in Boston, Computer Science Tutors in New York City

Popular Courses & Classes

GRE Courses & Classes in San Diego, Spanish Courses & Classes in Houston, ACT Courses & Classes in Los Angeles, GRE Courses & Classes in Los Angeles, SSAT Courses & Classes in Boston, GMAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Philadelphia, SSAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in San Diego, GMAT Courses & Classes in New York City

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Denver, SSAT Test Prep in Atlanta, GMAT Test Prep in Dallas Fort Worth, GMAT Test Prep in New York City, ACT Test Prep in San Diego, GRE Test Prep in Phoenix, SAT Test Prep in Denver, MCAT Test Prep in Miami, SAT 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 : Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #201 : Geometry

Example Question #3 : Calculating The Area Of A Quadrilateral

Example Question #91 : Quadrilaterals

Example Question #92 : Quadrilaterals

Example Question #12 : How To Find The Area Of A Rhombus

Example Question #391 : Advanced Geometry

Example Question #14 : Other Quadrilaterals

Example Question #15 : Other Quadrilaterals

Example Question #16 : Other Quadrilaterals

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

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details