Chapter 9.2, Problem 38E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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Each edge of a regular tetrahedron (see Exercise 37) has length

**a)** Show that the altitude of the tetrahedron measures

**b)** Show that the volume of the tetrahedron is

**c)** Find the volume of the tetrahedron if each side measures

To determine

**(a)**

**To show:**

The altitude of the tetrahedron measures

Explanation

**Given:**

Each edge of a regular tetrahedron 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

the sides of the triangular base measure

To determine

**(b)**

**To show:**

The volume of the tetrahedron is

To determine

**(c)**

**To find:**

The volume of the tetrahedron.

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