Chapter 9.2, Problem 37E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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

**a)** show that the area of each face is

**b)** show that the total area of the tetrahedron is

**c)** find the total area if each side measures

To determine

**(a)**

**To show:**

The area of each face is

Explanation

**Given:**

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

**Properties Used:**

The lateral area

In a regular pyramid, the lengths of the apothem

According to the Pythagorean theorem, in a right-angled triangle

Area of a right-angled triangle is

**Approach Used:**

i) Using the property

ii) Substitute the values of base and height

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

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

To determine

**(b)**

**To show:**

The total area of the tetrahedron is

To determine

**(c)**

**To find:**

The total area of the tetrahedron.

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