Call Now to Set Up Tutoring:

(888) 888-0446

Advanced Geometry : How to find the area of a trapezoid

Study concepts, example questions & explanations for Advanced Geometry

Create An Account

All Advanced Geometry Resources

6 Diagnostic Tests 57 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Trapezoids

Which of the following shapes is a trapezoid?

Shapes

Possible Answers:

C, D

None

B, C, D

B, D

Correct answer:

B, D

Explanation:

A trapezoid is a four-sided shape with straight sides that has a pair of opposite parallel sides. The other sides may or may not be parallel. A square and a rectangle are both considered trapezoids.

Report an Error

Example Question #1 : Trapezoids

What is the area of the following trapezoid?

Trapezoid

Possible Answers:

24m^2

80m^2

36m^2

40m^2

32m^2

Correct answer:

36m^2

Explanation:

The formula for the area of a trapezoid is:

$A = \frac{1}{2} (b_{1} + b_{2})(h)$ ,

where $b_{1}$ is the value of the top base, $b_{2}$ is value of the bottom base, and is the value of the height.

Plugging in our values, we get:

$A = \frac{1}{2} (8\: m + 10\: m)(4\: m)$

$A = \frac{1}{2} (18\: m)(4\: m)$

$A = (9\: m)(4\: m) = 36\: m^2$

Report an Error

Example Question #3 : Trapezoids

Screen_shot_2015-03-06_at_2.30.09_pm

What is the area of the trapezoid pictured above in square units?

Possible Answers:

238

119

168

Correct answer:

119

Explanation:

The formula for the area of a trapezoid is the average of the bases times the height,

$A=\frac{b_{1}+b_{2}}{2}h$ .

Looking at this problem and when the appropriate values are plugged in, the formula yields:

$A=(\frac{10+24}{2})7$

$A=\frac{34}{2}\cdot 7$

$A=\frac{238}{2}=119$

Report an Error

Example Question #4 : Trapezoids

Screen_shot_2015-03-06_at_2.44.49_pm

What is the height of the trapezoid pictured above?

Possible Answers:

Correct answer:

Explanation:

To find the height, we must introduce two variables, $b_{1}, b_{2}$ , each representing the bases of the triangles on the outside, so that $b_{1}+b_{2}+11=25, b_{1}+b_{2}=14$ . (Equation 1)

The next step is to set up two Pythagorean Theorems,

$13^2=b_{1}^2+h^2, 15^2=b_{2}^2+h^2$ (Equation 2, 3)

The next step is a substitution from the first equation,

$b_{1}=14-b_{2}, b_{1}^2=196-28b_{2}+b_{2}^2$ (Equation 4)

and plugging it in to the second equation, yielding

$13^2=196-28b_{2}+b_{2}^2+h^2$ (Equation 5)

The next step is to substitute from Equation 3 into equation 5,

$h^2=15^2-b_{2}^2$ , $169=196-28b_{2}+b_{2}^2+225-b_{2}^2$ which simplifies to

$-252=-28b_{2}, b_{2}=9$

Once we have one of the bases, just plug into the Pythagorean Theorem, 225=81+h^2, 144=h^2, h=12

Report an Error

Example Question #5 : Trapezoids

A isosceles trapezoid with sides , , , and has a height of , what is the area?

Possible Answers:

180

194

160

138

Correct answer:

180

Explanation:

An isosceles trapezoid has two sides that are the same length and those are not the bases, so the bases are 10 and 20.

The area of the trapezoid then is:

$A=\frac{b_{1}+b_{2}}{2}h=\frac{10+20}{2}12=15 \cdot 12=180$

Report an Error

Example Question #1 : Trapezoids

If the height of a trapezoid is , bottom base is , and the top base is , what is the area?

Possible Answers:

300

200

150

Correct answer:

150

Explanation:

The formula for finding the area of a trapezoid is:

$A=\frac{1}{2}(b1+b2)h$

Substitute the given values to find the area.

$A=\frac{1}{2}(20+10)(10)$

$A= \frac{1}{2}(30)(10)$

$A=\frac{1}{2}(300)$

A=150

Report an Error

Example Question #2 : Trapezoids

Find the area of a trapezoid with bases of length $12\:cm$ and $15\:cm$ and a height of $7\:cm$ .

Possible Answers:

$105\:cm^2$

$189\:cm^2$

$84\:cm^2$

$52.5\:cm^2$

$94.5\:cm^2$

Correct answer:

$94.5\:cm^2$

Explanation:

The formula for the area of a trapezoid is:

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

Where and are the bases and is the height. Using this formula and the given values, we get:

$A = \frac{12\:cm + 15\:cm}{2}\left ( 7\:cm) = 94.5\:cm^2$

Report an Error

Example Question #6 : Trapezoids

Find the area of a trapezoid with bases of $8\:cm$ and $11\:cm$ and a height of $14\:cm$ .

Possible Answers:

$88\:cm^2$

$133\:cm^2$

$112\:cm^2$

$66.5\:cm^2$

$121\:cm^2$

Correct answer:

$133\:cm^2$

Explanation:

The formula for the area of a trapezoid is:

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

Where and are the bases and is the height. Using this formula and the given values, we get:

$A = \frac{8\:cm + 12\:cm}{2}\left ( 14\:cm ) = 133\:cm^2$

Report an Error

Example Question #3 : Trapezoids

Trapezoid_1

Find the area of the above trapezoid.

Possible Answers:

$435\:units^2$

$208\:units^2$

$714\:units^2$

$195\:units^2$

$315\:units^2$

Correct answer:

$315\:units^2$

Explanation:

The formula for the area of a trapezoid is:

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

Where and are the bases and is the height. Using this formula and the given values, we get:

$A = \frac{13\:units + 29\:units}{2}\left ( 15\:units ) = 315\:units^2$

Report an Error

Example Question #4 : Trapezoids

Trapezoid_2

Find the area of the above trapezoid.

Possible Answers:

$50\:units^2$

$20\:units^2$

$40\:units^2$

$28\:units^2$

$35\:units^2$

Correct answer:

$28\:units^2$

Explanation:

The formula for the area of a trapezoid is:

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

Where and are the bases and is the height. Using this formula and the given values, we get:

$A = \frac{4\:units + 10\:units}{2}\left ( 4\:units\right ) = 28\:units^2$

Report an Error

View Tutors

Jack
Certified Tutor

University of Washington-Seattle Campus, Bachelor in Arts, Mathematics. Western Washington University, Master of Science, Mat...

View Tutors

Laura
Certified Tutor

New York University, Bachelor in Arts, French.

View Tutors

Sydni
Certified Tutor

Louisiana Tech University, Bachelor of Science, Finance. Louisiana Tech University, Master of Arts Teaching, Mathematics.

All Advanced Geometry Resources

6 Diagnostic Tests 57 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in Seattle, English Tutors in Seattle, Calculus Tutors in Phoenix, SAT Tutors in Boston, GMAT Tutors in Atlanta, ACT Tutors in Boston, SAT Tutors in Chicago, Physics Tutors in Boston, Algebra Tutors in Miami, Spanish Tutors in Miami

Popular Courses & Classes

GRE Courses & Classes in Washington DC, GMAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Phoenix, Spanish Courses & Classes in Atlanta, ISEE Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Boston, LSAT Courses & Classes in New York City, ACT Courses & Classes in Chicago, LSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Boston

Popular Test Prep

ACT Test Prep in Chicago, MCAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Miami, LSAT Test Prep in Atlanta, SAT Test Prep in Chicago, ISEE Test Prep in Philadelphia, GRE Test Prep in Miami, GMAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Phoenix, MCAT Test Prep in Seattle

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Advanced Geometry : How to find the area of a trapezoid

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #1 : Trapezoids

Example Question #1 : Trapezoids

Example Question #3 : Trapezoids

Example Question #4 : Trapezoids

Example Question #5 : Trapezoids

Example Question #1 : Trapezoids

Example Question #2 : Trapezoids

Example Question #6 : Trapezoids

Example Question #3 : Trapezoids

Example Question #4 : Trapezoids

All Advanced Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: