# math

what do you call a closed figure made up of line segments?

1. 👍
2. 👎
3. 👁
1. pentagon

1. 👍
2. 👎
2. ...isnt it polygon, not pentagon

1. 👍
2. 👎
3. What do you call a figure made up of "n" line segments?

Polygon

A polygon is a plane figure with three or more line segments and angles that are joined end to end so as to completely enclose an area without any of the line segments intersecting.

A convex polygon is one where the line segments joining any two points of the polygon remain totally inside the polygon, each interior angle being less than 180º.

A concave polygon is one where one or more line segments joining any two points of the polygon are outside of the polygon and one or more of the interior angles is greater than 180º. The inward pointing angle of a concave polygon is referred to as a reentrant angle. The angles less than 180º are called salient angles.

A regular polygon is one where all the sides have the same length and all the interior angles are equal.

A diagonal is a straight line connecting any two opposite vertices of the polygon.

Polygons are classified by the number of sides they have.

No. of sides.........Polygon Name
......3.....................Triangle
......5....................Pentogon
......6....................Hexagon
......7....................Heptagon
.....8......................Octagon
.....9......................Nonagon
....10.....................Decagon
....11....................Undecagon
....12....................Dodecagon
....13....................Tridecagon
......n........................n-gon

Regular Polygon Terminology

n = the number of sides

v = angle subtended at the center by one side = 360/n

s = the length of one side = R[2sin(v/2)] = r[2tan(v/2)]

R = the radius of the circumscribed circle = s[csc(v/2)]/2 = r[sec(v/2)]

r = the radius of the inscribed circle = R[cos(v/2)] = s[cot(v/2)]/2

a = apothem = the perpendicular distance from the center to a side (the radius of the inscribed circle)

p = the perimeter = ns

Area = s^2[ncot(v/2)]/4 = R^2[nsin(v/2)]/2 = r^2[ntan(v/2)]

The formula for the area of a regular polygon is also A = (1/2 )ap = (1/2)ans, where a is the apothem, p is the perimeter, s is the side length and n is the number of sides..

The sum of all the interior angles in a polygon is 180(n - 2)

The sum of the exterior angles in a polygon is 360º.

The internal angle between two adjacent sides of a regular polygon is given by 180(n - 2)/n

The external angle between any side and the extended adjacent side of a regular polygon is given by 360/n.

You might be interested in why the sum of all the interior angles of a polygon is 180(n - 2).
Consider first the square, rectangle and trapazoid. Draw one ofthe diagonals in each of these figures.
What is created is two triangles within each figure.
The sum of the interior angles of any triangle is 180 deg.
Therefore, the sum of the interior angles of each of these 4 sided figues is 360 Deg.
Now consider a pentagon with 5 sides that can be divided up into 3 triangles.
Therefore, the sum of the interior angles of a pentagon is 540 Deg.
What about a hexagon. I tink you will soonsee that the sum of the interior angles is 720 Deg.
Do you notice anything?
n = number of sides........3........4........5........6
Sum of Int. Angles.........180....360....540....720
The sum of the interior angles is representable by 180(n - 2).

Consider also the sum of the exterior angles.
Each exterior angle is 180 - 180(n - 2)/n = (180 - 180n + 360)/n = 360/n.
Therefore, the sum of the exterior angles is 360n/n or 360 Deg.

# Polygon Names (Prepared by AAC MrMaze, AAC Staff)

-- ---------------------
N N-gon
2 Digon
3 Trigon
(Equilateral Triangle)
4 Tetragon
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
(Enneagon)
10 Decagon
11 Undecagon
(Undegon, Hendecagon)
12 Dodecagon
(Duodecagon)
13 Tridecagon
Triskaidecagon)
(Tetrakaidecagon)
(Pentakaidecagon)
16 Hexdecagon
(Hexakaidecagon)
Heptakaidecagon)
(Octakaidecagon)
Enneakaidecagon)
20 Icosagon
21 Unaicosagon
22 Duoicosagon
23 Triskicosagon
24 Tetraicosagon
25 Pentaicosagon
26 Hexicosagon
27 Hepticosagon
28 Octicosagon
29 Nonicosagon
30 Triacontagon
40 Tetracontagon
50 Pentacontagon
60 Hexacontagon
70 Heptacontagon
80 Octacontagon
90 Enneacontagon
100 Hectogon
1000 Kiliagon
10000 Myriagon
infinite Circle

1. 👍
2. 👎

## Similar Questions

1. ### Math

1. Name one pair of congruent angles. (1 point) ∠PQR and ∠VST ∠PRQ and ∠SVT ∠RQP and ∠TVS ∠QPR and ∠STV 2. Name one pair of congruent sides. (1 point) Segments PR and SV Segments QR and ST Segments RP and TS

2. ### pre-algebra

Figure B is the image of Figure A. Which description explains how Figure A was transformed to create figure B. A. Figure A was Reflected across a horizontal line of reflection to create Figure B. B. Figure A was rotated 180 °

3. ### Math

My Answer = **** 1. Write the inequality for the graph. (1 point) image shows closed circle 4 and up. A. x > 4 B. x underscore > 4**** C. x underscore < 4 2. Write the inequality for the graph. image shows open circle up to both

4. ### geometry

Trisha drew a pair of line segments starting from a vertex. Which of these statements best compares the pair of line segments with the vertex? Answer A:Line segments have two endpoints and a vertex is a common endpoint where two

1. ### Geometry

Create a wrapping paper design that includes at least four of the following constructions: a bisected angle a perpendicular line drawn from a point not on a line to a line a perpendicular line drawn through a given point on a

2. ### Math: Geometry

2. Name four line. Segments that have point B as an endpoint. A. AF, CH, AE, BE B. BA, BF, BC, BH 3. AF, CH, AE, BE 4. BA , BF, BC, BH Please help!

3. ### Geometry

I have another question that stumped me Line segment AB with length a is divided by points P and Q into three line segments: AP , PQ, and QB , such that AP = 2PQ=2QB. Find: A)the distance between point A and the midpoints of the

4. ### Math

Is the dashed line a line of symmetry? An image shows a two dimensional arrow with a dashed line drawn down the middle of the arrow. (1 point) yes no 2. Is the dashed line a line of symmetry? figure (1 point) yes no 3. How many

1. ### Algebra

Two congruent figures are shown. Explanation: The figure on the left has vertices Upper A, Upper B, Upper C, Upper D, and Upper E. Line segment Upper Word AB is diagonally upward towards right, line segment Upper Word BC is

2. ### math

refer to the cube picture below, and use symbols such as AB to name the following: a. two parallel line segments? b. two line segments that do not lie in the same plane. c. two intersecting line segments d. three concurrent line

3. ### Math

If line A is a perpendicular bisector of MN, then which of the following statements is NOT true? 1)line A and MN intersect at a right angle 2)line A splits MN into two congruent segments 3)MN splits line A into two congruent

4. ### math help

I am a closed shape made of 6 line segments. I have 2 angles less than a right angle and no right angles. What shape am I? Draw an example in the workspace.