   Chapter 9.4, Problem 24E ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# A calendar is determined by using each of the 12 faces of a regular dodecahedron for one month of the year. With each side of the regular pentagonal face measuring 4cm, the area of each face is approximately 27.5   c m 2 .a) What is the total surface area of the calendar?b) If the material used to construct the calendar costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?

To determine

To find:

The total surface area of the calendar.

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:

Consider a calendar in the shape of a regular dodecahedron. A regular dodecahedron is a regular polyhedron with 12 congruent faces. Each face is a congruent pentagon.

A closed figure with five equal sides and angles is called a regular pentagon.

Area of each regular pentagon is 27.5 cm2.

The total surface area of the calendar:

Surface area of eac

To determine

To find:

The cost of the material used to construct a calendar

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