   Chapter 9.4, Problem 16E 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

Find the total area (surface area) of a regular dodecahedron (12 faces) if the area of each face is 6.4   c m 2 .

To determine

To find:

The total surface area of a regular dodecahedron.

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 dodecahedron is a regular polyhedron with 12 congruent faces. Each face is a congruent pentagon.

Surface area of each face of octahedron =6.4 cm2

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