4. Polygon DiagonalsA polygon is a closed figure bounded by line segments connecting the vertices (orcorners) of the polygon. For example, a 3-sided polygon has 3 vertices and is called atriangle, a 4-sided polygon has 4 vertices and is called a quadrilateral, etc. A diagonal ofa polygon is a line segment connecting two non-adjacent vertices. The followingdiagram provides an example of these terms.3 sides/0 diagonals/3vertices4 sides/2 diagonals/4vertices5 sides/5 diagonals/5 verticesa. Draw a 6-sided polygon and determine how many diagonals it has.b. How many diagonals are there in an 8-sided polygon? Explain clearly and completelyhow you arrived at your answer.c. How many diagonals are there in a 14-sided polygon? Explain clearly and completelyhow you arrived at your answer.d. How many diagonals are there in a 2-sided polygon? Explain clearly and completelyhow you arrived at your answer.

Given: A polygon is a closed figure bounded by line segments connecting the vertices of the polygon.…

a. Draw a 6-sided polygon and determine how many diagonals it has. b. How many diagonals are there in an 8-sided polygon? Explain clearly and completely how you arrived at your answer. c. How many diagonals are there in a 14-sided polygon? Explain clearly and completely how you arrived at your answer. d. How many diagonals are there in a 2-sided polygon? Explain clearly and completely how you arrived at your answer.

a. Draw a 6-sided polygon and determine how many diagonals it has. b. How many diagonals are there in an 8-sided polygon? Explain clearly and completely how you arrived at your answer. c. How many diagonals are there in a 14-sided polygon? Explain clearly and completely how you arrived at your answer. d. How many diagonals are there in a 2-sided polygon? Explain clearly and completely how you arrived at your answer.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

4. Polygon Diagonals
A polygon is a closed figure bounded by line segments connecting the vertices (or
corners) of the polygon. For example, a 3-sided polygon has 3 vertices and is called a
triangle, a 4-sided polygon has 4 vertices and is called a quadrilateral, etc. A diagonal of
a polygon is a line segment connecting two non-adjacent vertices. The following
diagram provides an example of these terms.
3 sides/0 diagonals/3vertices
4 sides/2 diagonals/4vertices
5 sides/5 diagonals/5 vertices
a. Draw a 6-sided polygon and determine how many diagonals it has.
b. How many diagonals are there in an 8-sided polygon? Explain clearly and completely
how you arrived at your answer.
c. How many diagonals are there in a 14-sided polygon? Explain clearly and completely
how you arrived at your answer.
d. How many diagonals are there in a 2-sided polygon? Explain clearly and completely
how you arrived at your answer.

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