Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

Create An Account

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Square

The perimeter of a square is half its area. What is the length of one side of the square?

Possible Answers:

$4\sqrt{2}$

Correct answer:

Explanation:

We begin by recalling the formulas for the perimeter and area of a square respectively.

P=4s

A=s^2

Using these formulas and the fact that the perimeter is half the area, we can create an equation.

$4s=\frac{1}{2}(s^2)$

We can multiply both sides by 2 to eliminate the fraction.

8s=s^2

To get one side of the equation equal to zero, we will move everything to the right side.

0=s^2-8s

Next we can factor.

0=s(s-8)

Setting each factor equal to zero provides two potential solutions.

s=0 or s-8=0

s=8

However, since a square cannot have a side of length 0, 8 is our only answer.

Report an Error

Example Question #1 : How To Find The Length Of The Side Of A Square

If the area of the square is 100 square units, what is, in units, the length of one side of the square?

Possible Answers:

Correct answer:

Explanation:

$Area = Length \times Length$

100 = (Length)^2

$Length = \sqrt{100}=10$

Report an Error

Example Question #1 : How To Find The Length Of The Side Of A Square

In Square SQUA , $SU = \sqrt{2x}$ . Evaluate in terms of .

Possible Answers:

$\sqrt{x}$

$2\sqrt{x}$

$x\sqrt{2}$

Correct answer:

$\sqrt{x}$

Explanation:

If diagonal $\overline{SU}$ of Square SQUA is constructed, then $\bigtriangleup SQU$ is a 45-45-90 triangle with hypotenuse $SU = \sqrt{2x}$ . By the 45-45-90 Theorem, the sidelength can be calculated as follows:

$SQ = \frac{SU}{\sqrt{2}} = \frac{\sqrt{2x}}{\sqrt{2}} = \sqrt{\frac{2x}{2}} = \sqrt{x}$ .

Report an Error

Example Question #1 : How To Find The Length Of The Side Of A Square

The circle that circumscribes Square SQUA has circumference 20. To the nearest tenth, evaluate .

Possible Answers:

9.0

3.2

2.3

6.4

4.5

Correct answer:

4.5

Explanation:

The diameter of a circle with circumference 20 is

$\frac{20}{\pi } \approx \frac{20 }{3.1416} \approx 6.3662$

The diameter of a circle that circumscribes a square is equal to the length of the diagonals of the square.

If diagonal $\overline{SU}$ of Square SQUA is constructed, then $\bigtriangleup SQU$ is a 45-45-90 triangle with hypotenuse approximately 6.3662. By the 45-45-90 Theorem, divide this by $\sqrt{2} \approx 1.4142$ to get the sidelength of the square:

$6.3662 \div 1.4142 \approx 4.5$

Report an Error

Example Question #1 : How To Find The Length Of The Side Of A Square

Rectangle RECT has area 90% of that of Square SQUA , and is 80% of . What percent of is ?

Possible Answers:

$79\frac{1}{81} \%$

$126 \frac{9}{16} \%$

$88 \frac{8} {9} \%$

$70 \%$

$112\frac{1}{2} \%$

Correct answer:

$88 \frac{8} {9} \%$

Explanation:

The area of Square SQUA is the square of sidelength , or $(SQ)^{2}$ .

The area of Rectangle RECT is $RE \cdot EC$ . Rectangle RECT has area 90% of that of Square SQUA , which is $\frac{9}{10} (SQ)^{2}$ ; is 80% of , so $RE = \frac{4}{5}SQ$ . We can set up the following equation:

$\frac{9}{10} (SQ)^{2} = RE \cdot EC$

$\frac{9}{10} (SQ)^{2} = \frac{4}{5} SQ \cdot EC$

$\frac{9}{10} \cdot SQ = \frac{4}{5} \cdot EC$

$\frac{10} {9} \cdot \frac{9}{10} \cdot SQ = \frac{10} {9} \cdot \frac{4}{5} \cdot EC$

$SQ = \frac{8} {9} \cdot EC$

As a percent, $\frac{8} {9}$ of is $\frac{8} {9} \times 100 \%= 88 \frac{8} {9} \%$

Report an Error

Example Question #931 : Basic Geometry

Reducing the area of a square by 12% has the effect of reducing its sidelength by what percent (hearest whole percent)?

Possible Answers:

$12 \%$

$3 \%$

$9 \%$

$6 \%$

$15 \%$

Correct answer:

$6 \%$

Explanation:

The area of the square was originally

$A = s^{2}$ ,

being the sidelength.

Reducing the area by 12% means that the new area is 88% of the original area, or 0.88A ; the square root of this is the new sidelength, so

$0.88A = 0.88s^{2}$

$\sqrt{0.88A} = \sqrt{0.88s^{2}} = \sqrt{0.88} \cdot \sqrt{s^{2}} \approx 0.94 s$

Each side of the new square will measure 94% of the length of the old measure - a reduction by 6%.

Report an Error

Example Question #1 : How To Find The Length Of The Side Of A Square

The circle inscribed inside Square SQUA has circumference 16. To the nearest tenth, evaluate .

Possible Answers:

7.2

5.1

3.6

10.2

2.5

Correct answer:

5.1

Explanation:

The diameter of a circle that is inscribed inside a square is equal to its sidelength , so all we need to do is find the diameter of the circle - which is circumference 16 divided by $\pi$ :

$\frac{16}{\pi } \approx \frac{16}{3.1416 } \approx 5.1$ .

Report an Error

Example Question #411 : Act Math

Thingy

Refer to the above figure, which shows equilateral triangle $\bigtriangleup CDE$ inside Square ABCD . Also, $\overline{EF} \perp \overline{AB}$ .

Quadrilateral BCEF has area 100. Which of these choices comes closest to ?

Possible Answers:

Correct answer:

Explanation:

Let s = CD , the sidelength shared by the square and the equilateral triangle.

The area of $\bigtriangleup CDE$ is

$\frac{s^{2}\sqrt{3}}{4} = \frac{\sqrt{3}}{4} \cdot s^{2} \approx \frac{1.7321}{4} \cdot s^{2} \approx 0.4330 s^{2}$

The area of Square ABCD is $s^{2}$ .

By symmetry, $\overline{EF}$ bisects the portion of the square not in the triangle, so the area of Quadrilateral BCEF is half the difference of those of the square and the triangle. Since the area of Quadrilateral BCEF is 100, we can set up an equation:

$\frac{1}{2}\left (s ^{2} - 0.4330 s ^{2} \right ) = 100$

$\frac{1}{2}\left ( 0.5670 s ^{2} \right ) = 100$

$0.2835 s ^{2} = 100$

$s ^{2} \approx 100 \div 0.2835$

$s ^{2} \approx 352.73$

$s \approx\sqrt{ 352.73} \approx 18.7$

Of the five choices, 20 comes closest.

Report an Error

Example Question #932 : Basic Geometry

The perimeter of a square is 444 . What is the length of one side of the square?

Possible Answers:

112

101

116

111

Correct answer:

111

Explanation:

Recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side length})$

By dividing both sides by , we can write the following:

$\text{Side length}=\frac{\text{Perimeter}}{4}$

For the square in question,

$\text{Side length}=\frac{444}{4}$

$\text{Side length}=111$

Report an Error

Example Question #521 : Quadrilaterals

The perimeter of a square is . What is the length of one side of the square?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the perimeter of a square:

$\text{Perimeter}=4(\text{side length})$

By dividing both sides by , we can write the following:

$\text{Side length}=\frac{\text{Perimeter}}{4}$

For the square in question,

$\text{Side length}=\frac{96}{4}$

$\text{Side length}=24$

Report an Error

View Tutors

Sophia
Certified Tutor

Universidad del Azuay, Bachelor in Arts, International Relations.

View Tutors

Mohammad Talha
Certified Tutor

University of Toronto, Mississauga, Bachelor, Chemistry, and Environmental Science.

View Tutors

Laura Jeanne
Certified Tutor

Texas Tech University, Bachelor in Arts, Music Teacher Education. Asbury Theological Seminary, Master of Divinity, Music Teac...

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Seattle, GRE Tutors in Miami, Calculus Tutors in Dallas Fort Worth, MCAT Tutors in Denver, SSAT Tutors in Phoenix, GMAT Tutors in Houston, English Tutors in San Francisco-Bay Area, SSAT Tutors in Boston, LSAT Tutors in Washington DC, GMAT Tutors in San Diego

Popular Courses & Classes

GMAT Courses & Classes in Los Angeles, GRE Courses & Classes in New York City, ACT Courses & Classes in Houston, Spanish Courses & Classes in Philadelphia, Spanish Courses & Classes in New York City, ISEE Courses & Classes in Phoenix, GMAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Miami

Popular Test Prep

GMAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Washington DC, MCAT Test Prep in Denver, ISEE Test Prep in San Francisco-Bay Area, SSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Miami, SAT Test Prep in Washington DC, LSAT Test Prep in Chicago, LSAT Test Prep in San Diego, GMAT 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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Basic Geometry : Quadrilaterals

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Square

Example Question #1 : How To Find The Length Of The Side Of A Square

Example Question #1 : How To Find The Length Of The Side Of A Square

Example Question #1 : How To Find The Length Of The Side Of A Square

Example Question #1 : How To Find The Length Of The Side Of A Square

Example Question #931 : Basic Geometry

Example Question #1 : How To Find The Length Of The Side Of A Square

Example Question #411 : Act Math

Example Question #932 : Basic Geometry

Example Question #521 : Quadrilaterals

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: