Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : How to find the surface area of a tetrahedron

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

If the edge length of a tetrahedron is $\sqrt3$ , what is the surface area of the tetrahedron?

Possible Answers:

$9\sqrt3$

$3\sqrt3$

$\sqrt6$

Correct answer:

$3\sqrt3$

Explanation:

Write the formula for finding the surface area of a tetrahedron.

$A=\sqrt3 s^2$

Substitute the edge and solve.

$A=\sqrt3 (\sqrt3)^2 = \sqrt3 (3) = 3\sqrt3$

Report an Error

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

Each of the faces of a regular tetrahedron has a base of $\small 11cm$ and a height of 9cm . What is the surface area of this tetrahedron?

Possible Answers:

220cm^2

198cm^2

154cm^2

180cm^2

99cm^2

Correct answer:

198cm^2

Explanation:

The surface area is the area of all of the faces of the tetrahedron. To begin, we must find the area of one of the faces. Because a tetrahedron is made up of triangles, we simply plug the given values for base and height into the formula for the area of a triangle:

$\small A=\frac{1}{2}bh$

$A=\frac{1}{2}(11cm)(9cm)$

A=49.5cm^2

Therefore, the area of one of the faces of the tetrahedron is 49.5cm^2 . However, because a tetrahedron has 4 faces, in order to find the surface area, we must multiply this number by 4:

$S.A.=4 \cdot 49.5cm^2$

$\small S.A.=198cm^2$

Therefore, the surface area of the tetrahedron is 198cm^2 .

Report an Error

Example Question #4 : Tetrahedrons

What is the surface area of a regular tetrahedron with a slant height of $\frac{\sqrt3}{2}$ ?

Possible Answers:

$\frac{3}{4}$

$\frac{3\sqrt3}{4}$

$\sqrt3$

$\sqrt4$

Cannot be determined

Correct answer:

$\sqrt3$

Explanation:

If this is a regular tetrahedron, then all four triangles are equilateral triangles.

If the slant height is $\frac{\sqrt3}{2}$ , then that equates to the height of any of the triangles being $\frac{\sqrt3}{2}$ .

In order to solve for the surface area, we can use the formula

$SA=\sqrt{3}\cdot a^2$

where in this case is the measure of the edge.

The problem has not given the edge; however, it has provided information that will allow us to solve for the edge and therefore the surface area.

Picture an equilateral triangle with a height $\frac{\sqrt3}{2}$ .
Tetrahedron

Drawing in the height will divide the equilateral triangle into two 30/60/90 right triangles. Because this is an equilateral triangle, we can deduce that finding the measure of the hypotenuse will suffice to solve for the edge length ().

In order to solve for the hypotenuse of one of the right triangles, either trig functions or the rules of the special 30/60/90 triangle can be used.

Using trig functions, one option is using $cos(30^{\circ})=\frac{\frac{\sqrt3}{2}}{a}$ .

Rearranging the equation to solve for ,

$a \cdot cos(30^{\circ}) = \frac{\sqrt3}{2}$

$a = \frac{\frac{\sqrt3}{2}}{cos(30^{\circ})}$

a = 1

Now that has been solved for, it can be substituted into the surface area equation.

$SA= \sqrt{3}\cdot (1)^2$

$SA= \sqrt{3} \cdot 1$

$SA = {\color{Blue} \sqrt{3}}$

Report an Error

Example Question #2 : Tetrahedrons

What is the surface area of a regular tetrahedron when its volume is 27?

Possible Answers:

64.9

6.12

46.8

136,368

136

Correct answer:

64.9

Explanation:

The problem is essentially asking us to go from a three-dimensional measurement to a two-dimensional one. In order to approach the problem, it's helpful to see how volume and surface area are related.

This can be done by comparing the formulas for surface area and volume:

$V= \frac{a^3}{6\sqrt{2}}$

$SA = \sqrt{3}\cdot a^2$

We can see that both calculation revolve around the edge length.

That means, if we can solve for (edge length) using volume, we can solve for the surface area.

$27=\frac{a^3}{6\sqrt{2}}$

$27 \cdot 6\sqrt{2}= a^3$

$\sqrt[3]{27 \cdot 6\sqrt{2}}=a$

${\color{Green} 6.12}=a$

Now that we know , we can substitute this value in for the surface area formula:

$SA=\sqrt{3} \cdot a^2$

$SA = \sqrt{3} \cdot (6.12)^2$

$SA={\color{Blue} 64.9}$

Report an Error

View ACT Math Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View ACT Math Tutors

Sarah
Certified Tutor

Broward College, Bachelor of Science, Business Administration and Management.

View ACT Math Tutors

Fitsum
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Biological and Physical Sciences.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

MCAT Courses & Classes in Chicago, ACT Courses & Classes in Miami, SSAT Courses & Classes in Miami, SSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Denver, MCAT Courses & Classes in Atlanta, ACT Courses & Classes in Phoenix, LSAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Denver, ACT Courses & Classes in Chicago

Popular Test Prep

ACT Test Prep in Philadelphia, MCAT Test Prep in San Diego, SSAT Test Prep in Los Angeles, MCAT Test Prep in Chicago, ISEE Test Prep in Atlanta, MCAT Test Prep in Seattle, ACT Test Prep in Phoenix, MCAT Test Prep in Washington DC, GMAT Test Prep in Houston, MCAT Test Prep in Los Angeles

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

ACT Math : How to find the surface area of a tetrahedron

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

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

Example Question #4 : Tetrahedrons

Example Question #2 : Tetrahedrons

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: