We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Prisms

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

A small rectangular jewelry box has two square ends with areas of 36 square centimeters, and a width of 10 centimeters. What is the surface area of the outside of the jewelry box.

Possible Answers:

$360 \; cm^2$

$240 \; cm^2$

$72 \; cm^2$

$216 \; cm^2$

$312 \; cm^2$

Correct answer:

$312 \; cm^2$

Explanation:

To find the surface area of the rectangular box we just need to add up the areas of all six sides. We know that two of the sides are 36 square centimeters, that means we need to find the areas of the four mising sides. To find the area of the missing sides we can just multiply the side of one of the squares (6 cm) by the width of the box:

$6 \times 10 = 60 \; cm^2$

But remember we have four of these rectangular sides:

$4 \times 60 = 240 \; cm^2$

Now we just add the two square sides and four rectangular sides to find the total surface area of the jewelry box:

$36 \; cm^2 + 36 \; cm^2 + 240 \; cm^2 = 312 \; cm^2$

That is the total surface area!

Report an Error

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

Alice is wrapping a rectangular box that measures $5\textup {in}\times 6\textup {in}\times 12\textup {in}$ . How many square feet of wrapping paper does she need?

Possible Answers:

$2.75 \textup{ ft}^{2}$

$2.00 \textup{ ft}^{2}$

$1.75\textup{ ft}^{2}$

$3.25\textup{ ft}^{2}$

$2.25\textup{ ft}^2$

Correct answer:

$2.25\textup{ ft}^2$

Explanation:

The surface area of a rectangular prism is given by

$\textup {SA=2lw+2lh+2wh}$ where is the length, is the width, and is the height.

Let $\textup l=5\textup { in}$ , $\textup {w}=6\textup{ in}$ , and $\textup {h}=12\textup { in}$

So the equation to solve becomes $\textup SA=2\cdot 5\cdot 6+2\cdot 5\cdot 12+2\cdot 6\cdot 12$ or $324\textup{ in}^{2}$

However the question asks for an answer in square feet. Knowing that $144\textup { in}^{2}=1\textup { ft}^{2}$ we can convert square inches to square feet. It will take $2.25\textup{ ft}^{2}$ of paper to wrap the present.

Report an Error

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

Find the surface area of the regular hexagonal prism.

Possible Answers:

1119.08

1248.67

1239.62

1339.05

Correct answer:

1239.62

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side}^2)$

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(10)^2+6(10)(12)=1239.62$

Make sure to round to places after the decimal.

Report an Error

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

Find the surface area of the regular hexagonal prism.

Possible Answers:

875.67

991.20

913.68

908.55

Correct answer:

908.55

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side}^2)$

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(8)^2+6(8)(12)=908.55$

Make sure to round to places after the decimal.

Report an Error

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

Find the surface area of the regular hexagonal prism.

Possible Answers:

800.61

885.00

809.67

751.36

Correct answer:

800.61

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side}^2)$

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(7)^2+6(7)(13)=800.61$

Make sure to round to places after the decimal.

Report an Error

Example Question #4 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

Possible Answers:

447.83

411.27

429.90

435.63

Correct answer:

429.90

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side}^2)$

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(5)^2+6(5)(10)=429.90$

Make sure to round to places after the decimal.

Report an Error

Example Question #11 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

Possible Answers:

842.61

845.59

839.07

862.24

Correct answer:

842.61

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side}^2)$

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(7)^2+6(7)(14)=842.61$

Make sure to round to places after the decimal.

Report an Error

Example Question #11 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

Possible Answers:

1406.37

1159.97

1828.25

1258.06

Correct answer:

1828.25

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side}^2)$

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(12)^2+6(12)(15)=1828.25$

Make sure to round to places after the decimal.

Report an Error

Example Question #11 : Prisms

Find the surface area of the regular hexagonal prism.

Possible Answers:

2197.80

2285.69

2159.63

2204.15

Correct answer:

2204.15

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side}^2)$

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(13)^2+6(13)(17)=2204.15$

Make sure to round to places after the decimal.

Report an Error

Example Question #14 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

Possible Answers:

648.52

679.34

655.06

620.39

Correct answer:

655.06

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side}^2)$

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(6)^2+6(6)(13)=655.06$

Make sure to round to places after the decimal.

Report an Error

View Tutors

Kaylee
Certified Tutor

Brigham Young University, Bachelor, MFA - Animation.

View Tutors

Lydia
Certified Tutor

The Richard Stockton College of New Jersey, Bachelor of Science, Biochemistry and Molecular Biology.

View Tutors

Michelle
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mathematics.

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Miami, Chemistry Tutors in New York City, Spanish Tutors in San Francisco-Bay Area, Reading Tutors in Dallas Fort Worth, English Tutors in Seattle, GRE Tutors in Seattle, Algebra Tutors in Miami, Physics Tutors in Chicago, Computer Science Tutors in Washington DC, LSAT Tutors in Boston

Popular Courses & Classes

ACT Courses & Classes in Chicago, SSAT Courses & Classes in New York City, SAT Courses & Classes in Philadelphia, ACT Courses & Classes in New York City, SSAT Courses & Classes in Miami, ISEE Courses & Classes in Houston, SSAT Courses & Classes in Houston, ACT Courses & Classes in Los Angeles, SSAT Courses & Classes in Seattle, ISEE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

GRE Test Prep in San Diego, ACT Test Prep in San Francisco-Bay Area, ACT Test Prep in Chicago, SAT Test Prep in Dallas Fort Worth, ACT Test Prep in Los Angeles, ISEE Test Prep in Boston, LSAT Test Prep in Denver, GMAT Test Prep in San Diego, ISEE Test Prep in Washington DC, MCAT Test Prep in San Francisco-Bay Area

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

Intermediate Geometry : Prisms

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

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

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

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

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

Example Question #4 : How To Find The Surface Area Of A Prism

Example Question #11 : How To Find The Surface Area Of A Prism

Example Question #11 : How To Find The Surface Area Of A Prism

Example Question #11 : Prisms

Example Question #14 : How To Find The Surface Area Of A Prism

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: