GMAT Math : Calculating the area of a right triangle

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 #272 : Geometry

In the above figure, triangle SPQ, SPR and PRQ are right triangles. Given the lengths of SP and PQ are 2cm. What is the area of triangle SPR?

Possible Answers:

Correct answer:

Explanation:

Since $\triangle SPQ,\triangle SPR,and\ \triangle PRQ$ are right triangles, we know that $\triangle SPQ$ is an isosceles right triangle. So we know that the lengths of $\overline{SP}$ and $\overline{PQ}$ are 2 cm, so we can get the length of $\overline{SQ}$ by using the Pythagorean Theorem:

$SQ =\sqrt{2^2+2^2}=\sqrt{8}$

is the midpoint of $\overline{SQ}$ , so the length of $\overline{SR}$ is $\sqrt{2}$ .

Now we can use the Pythagorean Theorem again to solve for $\overline{PR}$ : $\sqrt{ (2^2-(\sqrt2)^2)}=\sqrt2$ .

Finally, we have all the elements needed to solve for the area of $\triangle SPR$ :

$(1/2)*\sqrt2*\sqrt2=1$

Report an Error

Example Question #1 : Calculating The Area Of A Right Triangle

If a right triangle has a hypotenuse that is 10, and one side is 6, find the area of the triangle.

Possible Answers:

Correct answer:

Explanation:

Becaue this is a right triangle and since the hypotenuse is 10 and one side is 6, the other side will be 8. This can be found using the Pythagorean Theorem, or multiplying a 3-4-5 triangle by 2 to get a 6-8-10 triangle. Since the area of a right triangle is half of the product of the two sides, we have

$A=\frac{1}{2}L*W=\frac{1}{2}*6*8=24.$

Report an Error

Example Question #28 : Right Triangles

The hypotenuse of a $30 ^{\circ } - 60^{\circ } -90^{\circ }$ triangle is equal to the sidelength of a square. Give the ratio of the area of the square to that of the triangle.

Possible Answers:

$8\sqrt{3}:3$

16 :3

$16\sqrt{3}:3$

8 :3

4:1

Correct answer:

$8\sqrt{3}:3$

Explanation:

Let be the sidelength of the square. Then its area is $s ^{2}$ .

If the hypotenuse of a $30 ^{\circ } - 60^{\circ } -90^{\circ }$ triangle is , its shorter leg is half that, or $\frac{1}{2 }s$ ; its longer leg is $\sqrt{3}$ times the shorter leg, or $\frac{1}{2 }s \sqrt{3}$ . The area of the triangle is half the product of the legs, or

$\frac{1}{2} \cdot \frac{1}{2}s \cdot\frac{1}{2 }s \sqrt{3} =\frac{ \sqrt{3}}{8} s ^{2}$

The ratio of the area of the square to that of the triangle is

$s ^{2}: \frac{ \sqrt{3}}{8} s$ or $1: \frac{ \sqrt{3}}{8}$

or $8\sqrt{3}:3$

Report an Error

Example Question #2 : Calculating The Area Of A Right Triangle

A triangle on the coordinate plane has vertices (0,0), (c+1,0 ), (0,c-1) .

Which of the following expressions is equal to the area of the triangle?

Possible Answers:

$c^{2}$

$\frac{1}{2} c^{2}$

$\frac{1}{2} c^{2} -\frac{1}{2}$

$\frac{1}{2} c^{2} +\frac{1}{2}$

$c^{2} -1$

Correct answer:

$\frac{1}{2} c^{2} -\frac{1}{2}$

Explanation:

This is a right triangle with legs along the - and -axes, so the area of each can be calculated by taking one-half the product of the two legs.

The vertical leg has length c-1 ; the horizontal leg has length c+ 1 .

Now calculate the area:

$A = \frac{1}{2} bh = \frac{1}{2} (c-1)(c+1) = \frac{1}{2} (c^{2}-1) = \frac{1}{2} c^{2}- \frac{1}{2}$

Report an Error

Example Question #277 : Geometry

Calculate the area of the following right triangle, leave in terms of .

(Not drawn to scale.)

Possible Answers:

x^2+2x

x^2+3x+2

$\frac{x}{2}(x+2)$

$\frac{x}{2}(x+1)$

Correct answer:

$\frac{x}{2}(x+1)$

Explanation:

The equation for the area of a right triangle is:

$A=\frac{1}{2}b\times h$

In this case, our values are: b=x, h=(x+1)

Plugging this into the equation leaves us with:

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

which can be rewritten as $A=\frac{x}{2}(x+1)$

Report an Error

Example Question #4 : Calculating The Area Of A Right Triangle

A right triangle has a hypotenuse of 13 and a base of 12. Calculate the area of the triangle.

Possible Answers:

Correct answer:

Explanation:

In order to calculate the area of a right triangle, we need to know the height and the base. We are only given the length of the base, so we first need to use the Pythagorean theorem with the given hypotenuse to find the length of the height:

a^2+b^2=c^2

a^2=c^2-b^2=13^2-12^2=169-144

$a^2=25\rightarrow a=5$

Now that we have the height and the base, we can plug these values into the formula for the area of a right triangle:

$A=\frac{1}{2}bh=\frac{1}{2}(12)(5)=\frac{1}{2}(60)=30$

Report an Error

Example Question #2 : Calculating The Area Of A Right Triangle

Find the area of a triangle whose base is and height is .

Possible Answers:

Correct answer:

Explanation:

To find the area, use the following formula:

$A=\frac{1}{2}Bh=\frac{1}{2}(4)(8)=16$

Report an Error

All GMAT Math Resources

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

Popular Subjects

Chemistry Tutors in Atlanta, GMAT Tutors in Los Angeles, MCAT Tutors in New York City, Calculus Tutors in Denver, Computer Science Tutors in Boston, LSAT Tutors in San Diego, English Tutors in Miami, Statistics Tutors in Dallas Fort Worth, Statistics Tutors in San Francisco-Bay Area, English Tutors in Boston

Popular Courses & Classes

ISEE Courses & Classes in Boston, MCAT Courses & Classes in Washington DC, GMAT Courses & Classes in Washington DC, GMAT Courses & Classes in San Diego, ISEE Courses & Classes in Houston, ISEE Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Miami, ISEE Courses & Classes in Atlanta, SSAT Courses & Classes in Denver

Popular Test Prep

ISEE Test Prep in Houston, MCAT Test Prep in Los Angeles, LSAT Test Prep in Chicago, GRE Test Prep in Washington DC, LSAT Test Prep in Atlanta, ISEE Test Prep in Chicago, MCAT Test Prep in Philadelphia, SSAT Test Prep in Miami, SSAT Test Prep in Philadelphia, SAT Test Prep in San Diego

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 right triangle

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #272 : Geometry

Example Question #1 : Calculating The Area Of A Right Triangle

Example Question #28 : Right Triangles

Example Question #2 : Calculating The Area Of A Right Triangle

Example Question #277 : Geometry

Example Question #4 : Calculating The Area Of A Right Triangle

Example Question #2 : Calculating The Area Of A Right Triangle

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details