   Chapter 9.4, Problem 20E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

The total area (surface area) of a regular octahedron is 32 3   f t 2 . Find thea) area of each face.b) length of each edge.

To determine

a)

To find:

The area of each face.

Explanation

Approach:

1) A polygon is a two dimensional shape form with more than two straight lines.

2) A polyhedron is a three-dimensional solid shape.

3) Each flat surface of a polyhedron is a polygon and is called a face.

4) The line segment where two faces of a polyhedron meet is called an edge.

5) The point where three or more edges of a polyhedron meet is called a vertex.

6) A regular polyhedron is a convex polyhedron whose faces are congruent regular polygons.

Calculation:

A regular octahedron is a regular polyhedron with 8 congruent faces. Each face is an equilateral triangle.

Surface area of each face of octahedron =Total s

To determine

b)

To find:

The length of each edge.

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