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 #31 : How To Find The Area Of A Trapezoid

Find the area of the figure below.

Possible Answers:

150.36

148.78

161.57

132.67

Correct answer:

161.57

Explanation:

From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.

First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.

$\text{Hypotenuse}=\sqrt{\text{base}^2+\text{height}^2}$

$\text{Hypotenuse}=\sqrt{7^2+12^2}=\sqrt{193}$

Next, use this value to find the area of the trapezoid.

$\text{Area of Trapezoid}=\frac{1}{2}(\text{base 1}+\text{base 2})(\text{height})$

Plug in the given and found values to find the area.

$\text{Area of Trapezoid}=\frac{1}{2}(16+\sqrt{193})(8)=64+4\sqrt{193}$

Next, find the area of the triangle.

$\text{Area of Triangle}=\frac{1}{2}(\text{base})(\text{height})$

$\text{Area of Triangle}=\frac{1}{2}(7)(12)=42$

To find the area of the figure, add the two areas together.

$\text{Area of Figure}=\text{Area of Trapezoid}+\text{Area of Triangle}$

$\text{Area of Figure}=64+4\sqrt{193}+42=161.57$

Make sure to round to places after the decimal.

Report an Error

Example Question #31 : How To Find The Area Of A Trapezoid

Find the area of the figure below.

Possible Answers:

50.67

55.30

62.12

59.38

Correct answer:

62.12

Explanation:

From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.

First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.

$\text{Hypotenuse}=\sqrt{\text{base}^2+\text{height}^2}$

$\text{Hypotenuse}=\sqrt{5^2+11^2}=\sqrt{146}$

Next, use this value to find the area of the trapezoid.

$\text{Area of Trapezoid}=\frac{1}{2}(\text{base 1}+\text{base 2})(\text{height})$

Plug in the given and found values to find the area.

$\text{Area of Trapezoid}=\frac{1}{2}(11+\sqrt{146})(3)=\frac{33+3\sqrt{146}}{2}$

Next, find the area of the triangle.

$\text{Area of Triangle}=\frac{1}{2}(\text{base})(\text{height})$

$\text{Area of Triangle}=\frac{1}{2}(5)(11)=\frac{55}{2}$

To find the area of the figure, add the two areas together.

$\text{Area of Figure}=\text{Area of Trapezoid}+\text{Area of Triangle}$

$\text{Area of Figure}=\frac{33+3\sqrt{146}}{2}+\frac{55}{2}=62.12$

Make sure to round to places after the decimal.

Report an Error

Example Question #33 : How To Find The Area Of A Trapezoid

Find the area of the figure below.

Possible Answers:

803.92

898.53

877.23

906.39

Correct answer:

898.53

Explanation:

From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.

First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.

$\text{Hypotenuse}=\sqrt{\text{base}^2+\text{height}^2}$

$\text{Hypotenuse}=\sqrt{22^2+26^2}=\sqrt{1160}$

Next, use this value to find the area of the trapezoid.

$\text{Area of Trapezoid}=\frac{1}{2}(\text{base 1}+\text{base 2})(\text{height})$

Plug in the given and found values to find the area.

$\text{Area of Trapezoid}=\frac{1}{2}(34+\sqrt{1160})(18)=306+9\sqrt{1160}$

Next, find the area of the triangle.

$\text{Area of Triangle}=\frac{1}{2}(\text{base})(\text{height})$

$\text{Area of Triangle}=\frac{1}{2}(22)(26)=286$

To find the area of the figure, add the two areas together.

$\text{Area of Figure}=\text{Area of Trapezoid}+\text{Area of Triangle}$

$\text{Area of Figure}=306+9\sqrt{1160}+286=898.53$

Make sure to round to places after the decimal.

Report an Error

Example Question #371 : Advanced Geometry

Find the area of the figure below.

Possible Answers:

150.81

140.58

131.95

136.01

Correct answer:

150.81

Explanation:

From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.

First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.

$\text{Hypotenuse}=\sqrt{\text{base}^2+\text{height}^2}$

$\text{Hypotenuse}=\sqrt{9^2+10^2}=\sqrt{181}$

Next, use this value to find the area of the trapezoid.

$\text{Area of Trapezoid}=\frac{1}{2}(\text{base 1}+\text{base 2})(\text{height})$

Plug in the given and found values to find the area.

$\text{Area of Trapezoid}=\frac{1}{2}(13+\sqrt{181})(8)=52+4\sqrt{181}$

Next, find the area of the triangle.

$\text{Area of Triangle}=\frac{1}{2}(\text{base})(\text{height})$

$\text{Area of Triangle}=\frac{1}{2}(9)(10)=45$

To find the area of the figure, add the two areas together.

$\text{Area of Figure}=\text{Area of Trapezoid}+\text{Area of Triangle}$

$\text{Area of Figure}=52+4\sqrt{181}+45=150.81$

Make sure to round to places after the decimal.

Report an Error

Example Question #31 : Trapezoids

Find the area of the figure.

Possible Answers:

91.85

94.37

103.37

111.73

Correct answer:

111.73

Explanation:

From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.

First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.

$\text{Hypotenuse}=\sqrt{\text{base}^2+\text{height}^2}$

$\text{Hypotenuse}=\sqrt{7^2+12^2}=\sqrt{193}$

Next, use this value to find the area of the trapezoid.

$\text{Area of Trapezoid}=\frac{1}{2}(\text{base 1}+\text{base 2})(\text{height})$

Plug in the given and found values to find the area.

$\text{Area of Trapezoid}=\frac{1}{2}(14+\sqrt{193})(5)=35+\frac{5\sqrt{193}}{2}$

Next, find the area of the triangle.

$\text{Area of Triangle}=\frac{1}{2}(\text{base})(\text{height})$

$\text{Area of Triangle}=\frac{1}{2}(7)(12)=42$

To find the area of the figure, add the two areas together.

$\text{Area of Figure}=\text{Area of Trapezoid}+\text{Area of Triangle}$

$\text{Area of Figure}=35+\frac{5\sqrt{117}}{2}+42=111.73$

Make sure to round to places after the decimal.

Report an Error

Example Question #32 : How To Find The Area Of A Trapezoid

Trapezoid

Figure NOT drawn to scale.

Examine the above trapezoid.

MN = 20 , TM = MP = 5 , RM = MA

True, false, or inconclusive: the area of Trapezoid TRAP is 200.

Possible Answers:

False

True

Correct answer:

True

Explanation:

The area of a trapezoid is equal to one half the product of half the height of the trapezoid and the sum of the lengths of the bases. This is

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

$A = \frac{1}{2} \cdot TP \cdot (TR + PA)$

or, equivalently,

$A = TP \cdot \frac{TR + PA}{2}$

The height of the trapezoid is

TP = TM + MP = 5 + 5 = 10 .

The lengths of bases $\overline{TR}$ and $\overline{PA}$ are not given, so it might appear that determining the area of the trapezoid is impossible.

However, it is given that TM = MP and RM = MA - that is, the segment $\overline{MN}$ bisects both legs of the trapezoid. This makes $\overline{MN}$ the midsegment of the trapezoid, the length of which is the arithmetic mean of those of the bases:

$MN = \frac{TR+ PA}{2}$ .

Therefore, the formula for the area of the trapezoid can be rewritten as

$A = TP \cdot MN$ ,

the product of the height and the length of the midsegment.

TP = 10 and MN = 20 , so

$A =10 \cdot 20 = 200$ ,

making the statement true.

Report an Error

View Tutors

Abdullah
Certified Tutor

Ontario Tech University, Bachelor of Science, Mechanical Engineering.

View Tutors

Ebony
Certified Tutor

Johns Hopkins University, Masters in Education, Education.

View Tutors

Mayra
Certified Tutor

Universidad Interamericana de Puerto Rico, Bachelor in Arts, History Teacher Education. Caribbean University-Bayamon, Master ...

All Advanced Geometry Resources

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

Popular Subjects

GRE Tutors in Philadelphia, Math Tutors in Philadelphia, SSAT Tutors in Chicago, Reading Tutors in Miami, SAT Tutors in Chicago, English Tutors in San Diego, Computer Science Tutors in Houston, Biology Tutors in Atlanta, Biology Tutors in Washington DC, Chemistry Tutors in Washington DC

Popular Courses & Classes

ACT Courses & Classes in Boston, Spanish Courses & Classes in Boston, MCAT Courses & Classes in Phoenix, ACT Courses & Classes in San Diego, GMAT Courses & Classes in Washington DC, ISEE Courses & Classes in San Diego, ACT Courses & Classes in New York City, LSAT Courses & Classes in New York City, ACT Courses & Classes in Chicago, Spanish Courses & Classes in San Diego

Popular Test Prep

SSAT Test Prep in Chicago, SSAT Test Prep in Denver, SSAT Test Prep in Washington DC, ISEE Test Prep in Phoenix, MCAT Test Prep in New York City, SSAT Test Prep in Atlanta, LSAT Test Prep in Boston, ACT Test Prep in Houston, ISEE Test Prep in San Francisco-Bay Area, SSAT Test Prep in Dallas Fort Worth

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 #31 : How To Find The Area Of A Trapezoid

Example Question #31 : How To Find The Area Of A Trapezoid

Example Question #33 : How To Find The Area Of A Trapezoid

Example Question #371 : Advanced Geometry

Example Question #31 : Trapezoids

Example Question #32 : How To Find The Area Of A Trapezoid

All Advanced Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: