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 #531 : Gmat Quantitative Reasoning

If the area of an equilateral is , given a height of , what is the base of the triangle?

Possible Answers:

4.8

Correct answer:

4.8

Explanation:

We derive the equation of base of a triangle from the area of a triangle formula:

$A=\frac{bh}{2}$

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

$b=\frac{2*12}{5}$

b=4.8

Report an Error

Example Question #3 : Calculating The Length Of The Side Of An Equilateral Triangle

Export-png__3_

The height of an equilateral triangle ABC is . What is the length of side ?

Possible Answers:

$\frac{5}{\sqrt{3}}$

$2\sqrt{3}$

$\frac{10}{\sqrt{3}}$

$3\sqrt{5}$

Correct answer:

$\frac{10}{\sqrt{3}}$

Explanation:

Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by

$s=\frac{2h}{\sqrt{3}}$ , where is the length of the height.

Therefore, the final answer is

$\frac{2\cdot 5}{\sqrt3}=\frac{10}{\sqrt{3}}$ .

Report an Error

Example Question #1 : Equilateral Triangles

Export-png__5_

Equilateral triangle ABC is inscribed in a circle with radius , what is the length of a side of the triangle?

Possible Answers:

$\frac{15}{\sqrt{3}}$

$5\sqrt{3}$

$\frac{15}{2}$

$\sqrt{5}$

$3\sqrt{5}$

Correct answer:

$\frac{15}{\sqrt{3}}$

Explanation:

Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located $\frac{2}{3}$ away from the edge of a given height.

Therefore 5, the radius of the circle is $\frac{2}{3}$ of the height.

Therefore, the height must be $\frac{15}{2}$ .

From here, we can use the formula for the height of the equilateral triangle $h=s\frac{\sqrt{3}}{2}$ , where is the length of the height and is the length of a side of the equilateral triangle.

Therefore, $s=2\frac{h}{\sqrt{3}}$ , then $\frac{15}{\sqrt{3}}$ is the final answer.

Report an Error

Example Question #2 : Equilateral Triangles

Three straight sticks are gathered of exactly equal length. They are placed end to end on the ground to form a triangle. If the area of the triangle they form is 1.732 square feet. What is the length in feet of each stick?

Possible Answers:

$2\ feet$

$1\ foot$

$1.5\ feet$

$3\ feet$

$2.5\ feet$

Correct answer:

$2\ feet$

Explanation:

Equilateral_triangle

Let be the length of a side of an equilateral triangle. Then the formula for the area of an equilateral triangle with side is

$\frac{s^2\sqrt{3}}{4}$

So solving $1.732 = \frac{s^2\sqrt{3}}{4}$

we get s=2 .

Alternative Solution:

Without knowing this formula you can still use the Pythagorean Theorem to solve this. By drawing the height of the triangle, you split the triangle into 2 right triangles of equal size. The sides are the height, $\frac{s}{2}$ and . Letting stand for the unknown height, we solve

$(\frac{s}{2})^2 + h^2= s^2$ solving for we get

$h=\sqrt(s^2-(\frac{s}{2})^2) = \sqrt(s^2-\frac{s^2}{4}) = \sqrt(\frac{3s^2}{4}) = \frac{s\sqrt(3)}{2}$

The area for any triangle is the base times the height divided by 2. So

$1.732=\frac{sh}{2} = \frac{s(s\sqrt(3))}{2*2} = \frac{s^2\sqrt(3)}{4}$ or s=2 .

Report an Error

Example Question #2 : Equilateral Triangles

If an equilateral triangle has a side length of and a height of , what is the area of the given triangle?

Possible Answers:

Correct answer:

Explanation:

To find the area of a traingle, we need the height and base lengths. Plug the given values into the following formula:

$A= \frac{bh}{2}$

$= \frac{(3*2)}2 {}$

Report an Error

Example Question #2 : Equilateral Triangles

Export-png__3_

Triangle ABC is an equilateral triangle with side length . What is the area of the triangle?

Possible Answers:

$\frac{\sqrt{3}}{2}$

$\sqrt{3}$

$\frac{\sqrt{3}}{4}$

$2\sqrt{3}$

Correct answer:

$\sqrt{3}$

Explanation:

The area of an equilateral triangle is given by the following formula:

$\frac{s^{2}\sqrt{3}}{4}$ , where is the length of a side.

Since we know the length of the side, we can simply plug it in the formula and we have $\frac{4\sqrt{3}}{4}$ or $\sqrt{3}$ , which is the final answer.

Report an Error

Example Question #301 : Geometry

Export-png__5_

ABC is an equilateral triangle inscribed in a cirlce with radius . What is the area of the triangle ABC ?

Possible Answers:

$27\frac{\sqrt{5}}{4}$

$4\sqrt{3}$

$3\frac{\sqrt{3}}{4}$

$27\frac{\sqrt{3}}{4}$

Correct answer:

$27\frac{\sqrt{3}}{4}$

Explanation:

Since we are given a radius for the circle, we should be able to find the length of the height of the equilateral triangle, indeed, the center of the circle is $\frac{2}{3}$ of the length of the height from any vertex.

Therefore, the height is $3=\frac{2}{3}\cdot h$ where is the length of the height of the triangle. Therefore $h=\frac{9}{2}$ .

We can now plug in this value in the formula of the height of an equilateral triangle $h=s\frac{\sqrt{3}}{2}$ , where is the length of the side of the triangle.

Therefore, $s=\frac{9}{\sqrt{3}}$ or $3\sqrt{3}$ .

Now we should plug in this value into the formula for the area of an equilateral triangle $a=s^{2}\frac{\sqrt{3}}{4}$ where is the value of the area of the equilateral triangle. Therefore $a= 27\frac{\sqrt{3}}{4}$ , which is our final answer.

Report an Error

Example Question #5 : Equilateral Triangles

A given equilateral triangle has a side length and a height . What is the area of the triangle?

Possible Answers:

Not enough information provided

Correct answer:

Explanation:

For a given equilateral triangle with a side length and a height , the area is

$A=\frac{1}{2}bh$ . Plugging in the values provided:

$A=\frac{1}{2}(4)(7)$

$A=\frac{1}{2}(28)$

A=14

Report an Error

Example Question #6 : Equilateral Triangles

A given right triangle has a base length and a height . What is the area of the triangle?

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

For a given right triangle with a side length and a height , the area is

$A=\frac{1}{2}bh$ . Plugging in the values provided:

$A=\frac{1}{2}(5)(4)$

$A=\frac{1}{2}(20)$

A=10

Report an Error

Example Question #1 : Calculating The Area Of An Equilateral Triangle

A given right triangle has a base of length and a height . What is the area of the triangle?

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

For a given right triangle with a side length and a height , the area is

$A=\frac{1}{2}bh$ . Plugging in the values provided:

$A=\frac{1}{2}(9)(8)$

$A=\frac{1}{2}(72)$

A=36

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 Philadelphia, Chemistry Tutors in Phoenix, Algebra Tutors in Philadelphia, SSAT Tutors in Miami, LSAT Tutors in San Francisco-Bay Area, Chemistry Tutors in Los Angeles, Math Tutors in San Francisco-Bay Area, Statistics Tutors in San Diego, GRE Tutors in Miami, MCAT Tutors in Houston

Popular Courses & Classes

MCAT Courses & Classes in Denver, GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Washington DC, ISEE Courses & Classes in Washington DC, ACT Courses & Classes in Seattle, ISEE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Denver, Spanish Courses & Classes in Houston, LSAT Courses & Classes in New York City, ISEE Courses & Classes in Houston

Popular Test Prep

GMAT Test Prep in Houston, SSAT Test Prep in Washington DC, MCAT Test Prep in Dallas Fort Worth, ISEE Test Prep in San Francisco-Bay Area, ACT Test Prep in Seattle, GRE Test Prep in Phoenix, MCAT Test Prep in New York City, MCAT Test Prep in Denver, GMAT Test Prep in Dallas Fort Worth, SAT Test Prep in Miami

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 #531 : Gmat Quantitative Reasoning

Example Question #3 : Calculating The Length Of The Side Of An Equilateral Triangle

Example Question #1 : Equilateral Triangles

Example Question #2 : Equilateral Triangles

Example Question #2 : Equilateral Triangles

Example Question #2 : Equilateral Triangles

Example Question #301 : Geometry

Example Question #5 : Equilateral Triangles

Example Question #6 : Equilateral Triangles

Example Question #1 : Calculating The Area Of An Equilateral Triangle

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details