We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Geometry

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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:

$\$80$

$\$70$

$\$55$

$\$30$

$\$40$

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 #2 : How To Find The Area Of A Rectangle

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:

$\$225$

$\$280$

$\$310$

$\$120$

$\$350$

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:

$125\ ft^{2}$

$100\ ft^{2}$

$150\ ft^{2}$

$50\ ft^{2}$

$75\ ft^{2}$

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 #3 : How To Find The Area Of A Rectangle

The length of a rectangle is 5 times its width. Its width is 3 inches long. What is the area of the rectangle in square inches?

Possible Answers:

Correct answer: 45

Explanation:

The length is 5 x 3 = 15 inches. Multiplied by the width of 3 inches, yields 45 in².

Report an Error

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

A rectangle’s base is twice its height. If the base is 8” long, what is the area of the rectangle?

Possible Answers:

16 in²

24 in²

64 in²

32 in²

12 in²

Correct answer:

32 in²

Explanation:

Rectangle

B = 2H

B = 8”

H = B/2 = 8/2 = 4”

Area = B x H = 8” X 4” = 32 in²

Report an Error

Example Question #3 : How To Find The Area Of A Rectangle

The length of a rectangle is two more than twice the width. The perimeter is 58ft. What is the area of the rectangle?

Possible Answers:

$154 \; ft^{2}$

$138 \; ft^{2}$

$180 \; ft^{2}$

$198 \; ft^{2}$

$168 \; ft^{2}$

Correct answer:

$180 \; ft^{2}$

Explanation:

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

Let be equal to the width. We know that the length is equal to "two more than twice with width."

l=2w+2

The equation to solve for the perimeter becomes 58 = 2(2w + 2) + 2w .

58 = 4w + 4+2w=6w+4

54=6w

9=w

Now that we know the width, we can solve for the length.

l=2w + 2 = 20

Now we can find the area using A = lw .

A=(20ft)(9ft)=180ft^2

Report an Error

Example Question #31 : Rectangles

Rectangle

Find the area of a rectangle with a length of w=18in and a length of l=3.6ft .

Possible Answers:

$4.64ft^{2}$

$5.4 ft^{2}$

$4.5ft^{2}$

$6.44ft^{2}$

$64.8ft^{2}$

Correct answer:

$5.4 ft^{2}$

Explanation:

First, we need to convert the length and width of the rectangle into similiar units.

$w=\frac{18in}{1}*\frac{1ft}{12in}$

$\rightarrow 1.5ft$

Now, calculate the area.

A=l*w

A=3.6ft*1.5ft

$\rightarrow 5.4ft^{2}$

Report an Error

Example Question #215 : Geometry

Rectangle_with_diagonal

A rectangle has a diagonal of d=8cm and a width of w=5cm . What is the area of the rectangle?

Possible Answers:

$40.00cm^{2}$

Not enough information to solve

$\dpi{100} 31.22cm^{2}$

$22.31cm^{2}$

$26.26cm^{2}$

Correct answer:

$\dpi{100} 31.22cm^{2}$

Explanation:

We are given the rectangle's diagonal $\dpi{100} \dpi{100} (d=8cm)$ and width $\dpi{100} (w=5cm)$ and are asked to find its area. The diagonal forms two right triangles within the rectangle; therefore, we can use the Pythagorean theorem to find the length of the rectangle's missing side. Then we can use the formula A=l*w to find the are of the rectangle.

$a^{2}+b^{2}=c^{2}$

In our case, we can rename the variables to match our triangle.

$w^{2}+l^{2}=d^{2}$

$\dpi{100} \dpi{100} \dpi{100} (5cm)^{2}+l^{2}=(8cm)^{2}$

$\dpi{100} l^{2}=64cm^{2}-25cm^{2}$

$\dpi{100} \dpi{100} \dpi{100} \sqrt{l^{2}}=\sqrt{39cm^{2}}$

$\dpi{100} l=\sqrt{39cm^{2}}$

Now we can calculate the area.

$A=(\sqrt{39cm^{2}})*5cm$

$\rightarrow 31.22cm^{2}$

Report an Error

Example Question #32 : Rectangles

Joe has a rectangluar yard and wants to fence in his yard as well as plant grass seed. His yard measures $100\; ft\times 75\; ft$ . The fence costs $\$1.50$ per foot, and the grass seed costs $\$0.75$ per square foot. How much money does he need to complete both projects?

Possible Answers:

$\$4,325$

$\$6,150$

$\$4,575$

$\$5,625$

$\$5,100$

Correct answer:

$\$6,150$

Explanation:

This problem requires you to find both the perimeter (fence) and the area (grass seed) of a rectangle where $l=100\; ft$ and $w=75\; ft$ .

Fence Problem (Perimeter):

$2(l+w)(1.50)= 2(100+75)(1.50) = \$525.00$

Grass Seed Problem (Area):

$(l\cdot w)(0.75)=(100\cdot 75)(0.75)= \$5,625.00$

So the total cost for both projects is $\$6,150$ .

Report an Error

Example Question #31 : Rectangles

A rectangle has sides of 2x +1 units and units. If the perimeter of the rectangle is 104 units, what is its area?

Possible Answers:

728 units squared

154 units squared

units squared

315 units squared

209 units squared

Correct answer:

315 units squared

Explanation:

Since a rectangle has pairs of equal-length sides, multiplying each side by and adding the products together gives the perimeter of the rectangle. Use this fact to set up an equation with the given information about the rectangle's sides and perimeter. Solving for in this equation will provide necessary information for finding the rectangle's area:

2(2x+1) + 2(7) = 104

$\rightarrow 4x+2 + 14 = 104$

$\rightarrow 4x+ 16 = 104$

$\rightarrow 4x = 88$

$\rightarrow x = 22$

Multiplying the measure of the long side of the rectangle by the measure of the short side of the rectangle gives the rectangle's area. The length of the long side is given by substituting the solution for into the given expression 2x + 1 that defines its length. The short side is , giving the following equation to calculate the area:

$A = (2(22)+1) \times 7$

$\rightarrow A = 45 \times 7$

$\rightarrow A = 315$ units squared

Report an Error

View Tutors

Reena
Certified Tutor

View Tutors

Isabella
Certified Tutor

Iowa State University, Bachelor of Science, Mathematics.

View Tutors

Deeba
Certified Tutor

University of British Columbia, Bachelor in Arts, International Relations.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Miami, GMAT Tutors in Philadelphia, Physics Tutors in San Diego, Biology Tutors in Chicago, Math Tutors in New York City, GMAT Tutors in New York City, SSAT Tutors in San Diego, SAT Tutors in Philadelphia, Math Tutors in Philadelphia, Statistics Tutors in Seattle

Popular Courses & Classes

LSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Phoenix, ACT Courses & Classes in Miami, GMAT Courses & Classes in Miami, Spanish Courses & Classes in Miami, SAT Courses & Classes in Denver, Spanish Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Phoenix, Spanish Courses & Classes in Atlanta

Popular Test Prep

GMAT Test Prep in Washington DC, ISEE Test Prep in Boston, ACT Test Prep in Washington DC, SAT Test Prep in Denver, ACT Test Prep in Miami, SAT Test Prep in New York City, LSAT Test Prep in New York City, ISEE Test Prep in Atlanta, ACT Test Prep in San Francisco-Bay Area, SAT Test Prep in Philadelphia

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

High School Math : Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

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

Example Question #3 : How To Find The Area Of A Rectangle

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

Example Question #3 : How To Find The Area Of A Rectangle

Example Question #31 : Rectangles

Example Question #215 : Geometry

Example Question #32 : Rectangles

Example Question #31 : Rectangles

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: