Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Geometry

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Area Of A Rectangle

A rectangle has a width of 2x. If the length is five more than 150% of the width, what is the area of the rectangle?

Possible Answers:

5x + 10

6x² + 10x

5x + 5

10(x + 1)

6x² + 5

Correct answer:

6x² + 10x

Explanation:

Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.

A = lw = (3x + 5)(2x) = 6x² + 10x

Report an Error

Example Question #1 : How To Find The Area Of A Rectangle

Para-rec1

Rectangle ABCD is shown in the figure above. Points A and B lie on the graph of y = 64 – x² , and points C and D lie on the graph of y = x² – 36. Segments AD and BC are both parallel to the y-axis. The x-coordinates of points A and B are equal to –k and k, respectively. If the value of k changes from 2 to 4, by how much will the area of rectangle ABCD increase?

Possible Answers:

272

176

544

352

Correct answer:

176

Explanation:

Para-rec2

Para-rec3

Report an Error

Example Question #1 : How To Find The Area Of A Rectangle

George wants to paint the walls in his room blue. The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor. One gallon of paint covers 400 $ft^{2}$ and costs $40. One quart of paint covers 100 $ft^{2}$ and costs $15. How much money will he spend on the blue paint?

Possible Answers:

$\$40$

$\$55$

$\$80$

$\$30$

$\$70$

Correct answer:

$\$70$

Explanation:

The area of the walls is given by $A = 2wh + 2lh = 2(12)(10) + 2(15)(10) = 540 ft^{2}$

One gallon of paint covers 400 $ft^{2}$ and the remaining 140 $ft^{2}$ would be covered by two quarts.

So one gallon and two quarts of paint would cost $\$40 + \$15 + \$15 = \$70$

Report an Error

Example Question #184 : Plane Geometry

Daisy gets new carpet for her rectangluar room. Her floor is $21\ ft \times 24\ ft$ . The carpet sells for $5 per square yard. How much did she spend on her carpet?

Possible Answers:

$\$225$

$\$120$

$\$310$

$\$350$

$\$280$

Correct answer:

$\$280$

Explanation:

Since $3\ ft=1\ yd$ the room measurements are 7 yards by 8 yards. The area of the floor is thus 56 square yards. It would cost $5\cdot 56=\$280$ .

Report an Error

Example Question #2 : How To Find The Area Of A Rectangle

The length of a rectangular rug is five more than twice its width. The perimeter of the rug is 40 ft. What is the area of the rug?

Possible Answers:

$50\ ft^{2}$

$75\ ft^{2}$

$150\ ft^{2}$

$125\ ft^{2}$

$100\ ft^{2}$

Correct answer:

$75\ ft^{2}$

Explanation:

For a rectangle, $P=2w+2l$ and $A=lw$ where $w$ is the width and $l$ is the length.

Let $x=width$ and $2x+5=length$ .

So the equation to solve becomes $40=2x+2(2x+5)$ or $40=6x+10$ .

Thus $x=5\ ft$ and $2x+5=15\ ft$ , so the area is $75\ ft^{2}$ .

Report an Error

Example Question #1 : How To Find The Area Of A Rectangle

The front façade of a building is 100 feet tall and 40 feet wide. There are eight floors in the building, and each floor has four glass windows that are 8 feet wide and 6 feet tall along the front façade. What is the total area of the glass in the façade?

Possible Answers:

768 ft²

2464 ft²

1536 ft²

192 ft²

1536 ft²

Correct answer:

1536 ft²

Explanation:

Glass Area per Window = 8 ft x 6 ft = 48 ft²

Total Number of Windows = Windows per Floor * Number of Floors = 4 * 8 = 32 windows

Total Area of Glass = Area per Window * Total Number of Windows = 48 * 32 = 1536 ft²

Report an Error

Example Question #23 : Rectangles

Rectangle

Note: Figure NOT drawn to scale

AB = 13, BC = 7, AD = 9, DF = 3

What percent of Rectangle ACGF is pink?

Possible Answers:

$48\frac{3}{4} \%$

$46\frac{2}{3} \%$

$55 \frac{5}{9} \%$

$50 \%$

$44 \frac{4}{9} \%$

Correct answer:

$48\frac{3}{4} \%$

Explanation:

The pink region is Rectangle ABED . Its length and width are

L = AB = 13

W = AD = 9

so its area is the product of these, or

$A = 13 \times 9 = 117$ .

The length and width of Rectangle ACGF are

L = AC = AB + BC = 13+7 = 20

W =AF = AD + DF=9+3 = 12

so its area is the product of these, or

$20 \times 12 = 240$ .

We want to know what percent 117 is of 240, which can be answered as follows:

$\frac{117}{240} \times 100 \% = 48\frac{3}{4} \%$

Report an Error

Example Question #24 : Rectangles

Rectangle

Note: Figure NOT drawn to scale

Refer to the above diagram.

40% of Rectangle ACGF is pink. AB = 20, AD = 15, BC = 10 .

Evaluate .

Possible Answers:

DF = 12

DF = 5

DF = 15

DF = 8

DF = 10

Correct answer:

DF = 10

Explanation:

Rectangle ABED has length L = AB = 20 and width W = AD = 15 , so it has area

$LW = 20 \times 15 = 300$ .

300 is 40% of, or 0.40 times, the area of Rectangle ACGF , which we will call . We can determine as follows:

0.40 A = 300

$A = 300 \div 0.4 = 750$ .

The length of Rectangle ACGF is

L = AC = AB + BC = 20 + 10 = 30 ,

so its width is

$W = AF = 750 \div 30 = 25$ .

Since

W = AF= AD + DF ,

25 = 15 + DF

DF = 10

Report an Error

Example Question #323 : Plane Geometry

Rectangle

Note: Figure NOT drawn to scale

AB = 24, BC = 6, AD = 12, DF = 3

What percent of Rectangle ACGF is white?

Possible Answers:

$40 \%$

$25 \%$

$36 \%$

$33 \frac{1}{3} \%$

$44 \frac{4}{9} \%$

Correct answer:

$36 \%$

Explanation:

The pink region is Rectangle ABED . Its length and width are

L = AB = 24

W = AD = 12

so its area is the product of these, or

$24 \times 12 = 288$ .

The length and width of Rectangle ACGF are

L = AC = AB + BC = 24 + 6 =30

W =AF = AD + DF= 12 + 3 = 15

so its area is the product of these, or

$30 \times 15 = 450$ .

The white region is Rectangle ABED cut from Rectangle ACGF , so its area is the difference of the two:

450 - 288 = 162 .

So we want to know what percent 162 is of 450, which can be answered as follows:

$\frac{162}{450} \times 100 \% = 36 \%$

Report an Error

Example Question #13 : How To Find The Area Of A Rectangle

Rectangle

Note: Figure NOT drawn to scale

AB = 20, BC = 8, AD = 10, DF = 4

Give the ratio of the perimeter of Rectangle ACGF to that of Rectangle ABED .

Possible Answers:

5:3

2:1

5:2

4:3

7:5

Correct answer:

7:5

Explanation:

The perimeter of Rectangle ABED is

P = AB +BE + ED + AD

Opposite sides of a rectangle are congruent, so

AB= ED = 20, AD = BE = 10

and

P = 20 + 10 + 20 + 10 = 60

The perimeter of Rectangle ACGF is

P = AC + CG + GF + AF

Opposite sides of a rectangle are congruent, so

GF = AC = AB + BC = 20 + 8 = 28 ,

CG = AF = AD + DF = 10 + 4 = 14 ,

and

P = 28 + 14+ 28 + 14= 84

The ratio of the perimeters is

$\frac{84}{60} = \frac{84 \div 12}{60 \div 12} = \frac{7}{5}$ - that is, 7 to 5.

Report an Error

View PSAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

View PSAT Mathematics Tutors

Keith
Certified Tutor

Xavier University, Bachelor in Business Administration, Accounting. Ohio University-Main Campus, Masters in Education, Mathem...

View PSAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Denver, GRE Tutors in Los Angeles, Calculus Tutors in Philadelphia, Calculus Tutors in Chicago, MCAT Tutors in Phoenix, Reading Tutors in Boston, ISEE Tutors in New York City, SAT Tutors in San Diego, Math Tutors in Atlanta, Calculus Tutors in San Francisco-Bay Area

Popular Courses & Classes

ACT Courses & Classes in San Diego, SSAT Courses & Classes in San Diego, GRE Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Boston, SSAT Courses & Classes in Atlanta, GRE Courses & Classes in Seattle, GMAT Courses & Classes in Los Angeles, SAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Chicago

Popular Test Prep

LSAT Test Prep in Miami, ISEE Test Prep in Philadelphia, LSAT Test Prep in Phoenix, GRE Test Prep in San Francisco-Bay Area, SAT Test Prep in Chicago, ACT Test Prep in San Diego, ISEE Test Prep in Chicago, MCAT Test Prep in Chicago, LSAT Test Prep in Los Angeles, MCAT Test Prep in Boston

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

PSAT Math : Geometry

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Find The Area Of A Rectangle

Example Question #1 : How To Find The Area Of A Rectangle

Example Question #1 : How To Find The Area Of A Rectangle

Example Question #184 : Plane Geometry

Example Question #2 : How To Find The Area Of A Rectangle

Example Question #1 : How To Find The Area Of A Rectangle

Example Question #23 : Rectangles

Example Question #24 : Rectangles

Example Question #323 : Plane Geometry

Example Question #13 : How To Find The Area Of A Rectangle

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: