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Math
GeometryElementary Geometry for College Students6th Edition

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

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

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Problem 1E
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Problem 6E
Problem 7E
Problem 8E
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Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 27E
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Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
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Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
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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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Chapter 9.4,
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Chapter 9.4,
Problem 25E
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Sect-9.1 P-1ESect-9.1 P-2ESect-9.1 P-3ESect-9.1 P-4ESect-9.1 P-5ESect-9.1 P-6ESect-9.1 P-7ESect-9.1 P-8ESect-9.1 P-9ESect-9.1 P-10E
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