Chapter 9.4, Problem 24E

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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

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

The total surface area of the calendar:

To determine

**To find:**

The cost of the material used to construct a calendar

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