menu
bartleby
search
close search
Hit Return to see all results
Subscribe
Sign in

Math
GeometryElementary Geometry for College Students6th Edition

close solutoin list
Chapter 9.2, Problem 37E
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

A regular tetrahedron is a regular triangular pyramid in which all faces (lateral faces and base) are congruent. If each edge has length e ,

a) show that the area of each face is A = e 2 3 4 .

b) show that the total area of the tetrahedron is T = e 2 3 .

c) find the total area if each side measures e = 4 i n .

Chapter 9.2, Problem 37E, A regular tetrahedron is a regular triangular pyramid in which all faces lateral faces and base are

To determine

(a)

To show:

The area of each face is A=e234.

Explanation

Given:

A regular triangular pyramid in which all faces (lateral faces and base) are congruent and each edge has length e as below,

Properties Used:

The lateral area L of a regular pyramid with slant height of length l and perimeter P of the base is given by

L=12lP.

In a regular pyramid, the lengths of the apothem a of the base, the altitude h, and the slant height l satisfy the Pythagorean Theorem; that is, l2=a2+h2.

According to the Pythagorean theorem, in a right-angled triangle hypotenuse2=base2+perpendicular2.

Area of a right-angled triangle is 12×base×height.

Approach Used:

i) Using the property l2=a2+h2, find the height or altitude h by substituting the values of l and a.

ii) Substitute the values of base and height h in equation 12×base×height to get the area of each lateral face since it is a triangular pyramid.

iii) Compare the given value with the value from step (ii).

Calculation:

From the given figure

the sides of the square base and lateral edge all are e.

Considering the right-angled triangle with triangle base and slant height e

To determine

(b)

To show:

The total area of the tetrahedron is T=e23.

To determine

(c)

To find:

The total area of the tetrahedron.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution
arrow_back
Chapter 9.2,
Problem 36E
Chapter 9.2,
Problem 38E
arrow_forward

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 9 Solutions

Show all chapter solutions add
Sect-9.1 P-1ESect-9.1 P-2ESect-9.1 P-3ESect-9.1 P-4ESect-9.1 P-5ESect-9.1 P-6ESect-9.1 P-7ESect-9.1 P-8ESect-9.1 P-9ESect-9.1 P-10E
Sect-9.1 P-11ESect-9.1 P-12ESect-9.1 P-13ESect-9.1 P-14ESect-9.1 P-15ESect-9.1 P-16ESect-9.1 P-17ESect-9.1 P-18ESect-9.1 P-19ESect-9.1 P-20ESect-9.1 P-21ESect-9.1 P-22ESect-9.1 P-23ESect-9.1 P-24ESect-9.1 P-25ESect-9.1 P-26ESect-9.1 P-27ESect-9.1 P-28ESect-9.1 P-29ESect-9.1 P-30ESect-9.1 P-31ESect-9.1 P-32ESect-9.1 P-33ESect-9.1 P-34ESect-9.1 P-35ESect-9.1 P-36ESect-9.1 P-37ESect-9.1 P-38ESect-9.1 P-39ESect-9.1 P-40ESect-9.1 P-41ESect-9.1 P-42ESect-9.1 P-43ESect-9.1 P-44ESect-9.1 P-45ESect-9.1 P-46ESect-9.1 P-47ESect-9.2 P-1ESect-9.2 P-2ESect-9.2 P-3ESect-9.2 P-4ESect-9.2 P-5ESect-9.2 P-6ESect-9.2 P-7ESect-9.2 P-8ESect-9.2 P-9ESect-9.2 P-10ESect-9.2 P-11ESect-9.2 P-12ESect-9.2 P-13ESect-9.2 P-14ESect-9.2 P-15ESect-9.2 P-16ESect-9.2 P-17ESect-9.2 P-18ESect-9.2 P-19ESect-9.2 P-20ESect-9.2 P-21ESect-9.2 P-22ESect-9.2 P-23ESect-9.2 P-24ESect-9.2 P-25ESect-9.2 P-26ESect-9.2 P-27ESect-9.2 P-28ESect-9.2 P-29ESect-9.2 P-30ESect-9.2 P-31ESect-9.2 P-32ESect-9.2 P-33ESect-9.2 P-34ESect-9.2 P-35ESect-9.2 P-36ESect-9.2 P-37ESect-9.2 P-38ESect-9.2 P-39ESect-9.2 P-40ESect-9.2 P-41ESect-9.2 P-42ESect-9.2 P-43ESect-9.2 P-44ESect-9.2 P-45ESect-9.3 P-1ESect-9.3 P-2ESect-9.3 P-3ESect-9.3 P-4ESect-9.3 P-5ESect-9.3 P-6ESect-9.3 P-7ESect-9.3 P-8ESect-9.3 P-9ESect-9.3 P-10ESect-9.3 P-11ESect-9.3 P-12ESect-9.3 P-13ESect-9.3 P-14ESect-9.3 P-15ESect-9.3 P-16ESect-9.3 P-17ESect-9.3 P-18ESect-9.3 P-19ESect-9.3 P-20ESect-9.3 P-21ESect-9.3 P-22ESect-9.3 P-23ESect-9.3 P-24ESect-9.3 P-25ESect-9.3 P-26ESect-9.3 P-27ESect-9.3 P-28ESect-9.3 P-29ESect-9.3 P-30ESect-9.3 P-31ESect-9.3 P-32ESect-9.3 P-33ESect-9.3 P-34ESect-9.3 P-35ESect-9.3 P-36ESect-9.3 P-37ESect-9.3 P-38ESect-9.3 P-39ESect-9.3 P-40ESect-9.3 P-41ESect-9.3 P-42ESect-9.3 P-43ESect-9.3 P-44ESect-9.3 P-45ESect-9.3 P-46ESect-9.3 P-47ESect-9.3 P-48ESect-9.3 P-49ESect-9.4 P-1ESect-9.4 P-2ESect-9.4 P-3ESect-9.4 P-4ESect-9.4 P-5ESect-9.4 P-6ESect-9.4 P-7ESect-9.4 P-8ESect-9.4 P-9ESect-9.4 P-10ESect-9.4 P-11ESect-9.4 P-12ESect-9.4 P-13ESect-9.4 P-14ESect-9.4 P-15ESect-9.4 P-16ESect-9.4 P-17ESect-9.4 P-18ESect-9.4 P-19ESect-9.4 P-20ESect-9.4 P-21ESect-9.4 P-22ESect-9.4 P-23ESect-9.4 P-24ESect-9.4 P-25ESect-9.4 P-27ESect-9.4 P-28ESect-9.4 P-29ESect-9.4 P-30ESect-9.4 P-31ESect-9.4 P-32ESect-9.4 P-33ESect-9.4 P-34ESect-9.4 P-35ESect-9.4 P-36ESect-9.4 P-37ESect-9.4 P-38ESect-9.4 P-39ESect-9.4 P-40ESect-9.4 P-41ESect-9.4 P-42ESect-9.4 P-43ESect-9.4 P-44ESect-9.4 P-45ESect-9.4 P-46ESect-9.4 P-47ESect-9.4 P-48ESect-9.4 P-49ESect-9.4 P-50ESect-9.CR P-1CRSect-9.CR P-2CRSect-9.CR P-3CRSect-9.CR P-4CRSect-9.CR P-5CRSect-9.CR P-6CRSect-9.CR P-7CRSect-9.CR P-8CRSect-9.CR P-9CRSect-9.CR P-10CRSect-9.CR P-11CRSect-9.CR P-12CRSect-9.CR P-13CRSect-9.CR P-14CRSect-9.CR P-15CRSect-9.CR P-16CRSect-9.CR P-17CRSect-9.CR P-18CRSect-9.CR P-19CRSect-9.CR P-20CRSect-9.CR P-21CRSect-9.CR P-22CRSect-9.CR P-23CRSect-9.CR P-24CRSect-9.CR P-25CRSect-9.CR P-26CRSect-9.CR P-27CRSect-9.CR P-28CRSect-9.CR P-29CRSect-9.CR P-30CRSect-9.CR P-31CRSect-9.CR P-32CRSect-9.CT P-1CTSect-9.CT P-2CTSect-9.CT P-3CTSect-9.CT P-4CTSect-9.CT P-5CTSect-9.CT P-6CTSect-9.CT P-7CTSect-9.CT P-8CTSect-9.CT P-9CTSect-9.CT P-10CTSect-9.CT P-11CTSect-9.CT P-12CTSect-9.CT P-13CTSect-9.CT P-14CTSect-9.CT P-15CTSect-9.CT P-16CT

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Writing Vectors in Terms of i and j Write the given vector in terms of i and j. 28. u = 2, 10

Precalculus: Mathematics for Calculus (Standalone Book)

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Finite Mathematics and Applied Calculus (MindTap Course List)

Find the appropriate measure of central tendency for each variable displayed in problem 2.5. Report each statis...

Essentials Of Statistics

For the foUow.ing population of N=6 score: l ,4,33,4 Sketch a histogram showing the population distribution. Lo...

Statistics for The Behavioral Sciences (MindTap Course List)

Find an equation of the straight line that passes through the point (1, 3) and is parallel to the line passing ...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Evaluate each expression: 28/27(6+10)/(62)

Elementary Technical Mathematics

Determine the set of points at which the function is continuous. 33. G(x,y)=x+1x2y2

Multivariable Calculus

Expand each expression in Exercises 122. (x+yxy)2

Finite Mathematics

In Problems 5-10, use the indicated x-values on the graph of to find the following. 5. Find intervals over wh...

Mathematical Applications for the Management, Life, and Social Sciences

Experiments show that if the chemical reaction N2O2NO2+12O2 takes place at 45C, the rate of reaction of dinitro...

Single Variable Calculus: Early Transcendentals, Volume I

Critical Region Method: Testing Proportions Solve Problem 17 using the critical region method of testing. Hint:...

Understanding Basic Statistics

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. 6x(x2...

Applied Calculus

Based on data from a dart-throwing experiment, the article Shooting Darts (Chance, Summer 1997, 1619)proposed t...

Probability and Statistics for Engineering and the Sciences

Finding a Derivative In Exercises 13-32, find the derivative of the function. y=5(2x3)4

Calculus: Early Transcendental Functions

Use inductive reasoning and the data in the inclined plane time-distance table, shown above exercise 17 predict...

Mathematical Excursions (MindTap Course List)

For Problems 33-42, list the elements of each set. For example, the elements of x|x is a natural number less th...

Intermediate Algebra

Find the functions (a) f g, (b) g f, (c) f f, and (d) g g and their domains. 36. f(x) = sin x, g(x) = x2 + ...

Calculus: Early Transcendentals

If g is the inverse function of f(x)=2x+Inx, find g(2).

Calculus (MindTap Course List)

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or gi...

Single Variable Calculus

Finding Limits In Exercises 37-58, find the limit (if it exists). See Examples 5, 6, 7, 9, and 11. limx2x2+3x-1...

Calculus: An Applied Approach (MindTap Course List)

In Exercises, let the binary operation be defined on by the given rule. Determine in each case whether a grou...

Elements Of Modern Algebra

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters) after t seconds...

Single Variable Calculus: Early Transcendentals

Change each of the following to decimal degrees. If rounding is necessary, round to the nearest hundredth of a ...

Trigonometry (MindTap Course List)

Using the Limit Comparison Test In Exercises 17-26, use the Limit Comparison Test to determine the convergence ...

Calculus of a Single Variable

Use the pie chart What is Your Favorite Cookie? to find the decimal and reduced fraction equivalent for exercis...

Contemporary Mathematics for Business & Consumers

A 5400-pound sports utility vehicle is parked on an 180 slope. Assume the only force to overcome is that due to...

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 110, find the graphical solution to each inequality. 3x+4y2

Finite Mathematics for the Managerial, Life, and Social Sciences

If n = 21 and k = 10, for what values of R2 would adjusted R2 be negative?

Introduction To Statistics And Data Analysis

Queuing Model The average length of time that a customer waits in line for service is W(x,y)=1xy,xy where is d...

Multivariable Calculus

Finding the Area of a Region In Exercises 3740, find the area of the given region. y=xx2

Calculus

Graph each point. Indicate the quadrant in which the point lies or the axis on which it lies. (0,7)

College Algebra (MindTap Course List)

True or False: If h'(x) = k(x), then k(x) is an antiderivative of h(x).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

In this chapter, we described a study in which Skjoeveland (2001) examined the effect of street parks on social...

Research Methods for the Behavioral Sciences (MindTap Course List)

Express the following degrees, minutes, and seconds as decimal degrees. Round the answer to 4 decimal places. 1...

Mathematics For Machine Technology

What information should be included in the abstract of an APA-style research report?

Research Methods for the Behavioral Sciences (MindTap Course List)

Consider a binomial experiment with n = 10 and p = .10. a. Compute f(0). b. Compute f(2). c. Compute P(x 2). d...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the p...

Statistics for Business & Economics, Revised (MindTap Course List)

Finding Intercepts In Exercises 1-4, find any intercepts. y=(x3)x+4

Calculus (MindTap Course List)

Find a definite integral for the area of the surface of revolution about the x-axis obtained by rotating the cu...

Study Guide for Stewart's Multivariable Calculus, 8th

bartleby
© bartleby 2019