Polygons A closed figure formed by a finite number of coplanar segments such that: 1.The sides that...

PolygonsPolygons

A closed figure formed by a finite number of coplanar segments such that:

1.The sides that have a common endpoint are noncollinear, and

2.Each side intersects exactly two other sides, but only at their endpoints

A polygon is named by the letters of its vertices, written in consecutive order.

Polygon ABC or CBA

Polygon WXYZ or YZWX, etc.

Polygon EFGHJK or HGFEKJ, etc.

Concave or ConvexConcave or Convex

There are two types of polygons:

Concave: Any side which is extended contains points in the interior of the polygon.

Convex: Any side which is extended contains no point in the interior of the polygon.

At least one side is “caved” in.

Special NamesSpecial NamesPolygons can be classified by the number

of sides they have:

Regular PolygonRegular Polygon

VUWVUTPWQPRQSRTSUT

UVWPQRST

A convex polygon in which all sides are congruent and all angles are congruent

Example 1Example 1

Number of Sides:

Name:

Convex or Concave?

Regular or Irregular?

Number of Sides:

Name:

Convex or Concave?

Regular or Irregular?

5

pentagon

Convex

Regular

8

Octagon

Concave

Irregular; WHY?

PerimeterPerimeter

The sum of the lengths of the sides of a polygon.

Some polygons have “shortcut” formulas:

Example 2Example 2

Example 3Example 3

First, use the distance formula to calculate the side lengths, then find the perimeter. 2

122

12 yyxxd

5254115 22 PQd

13168461 22 QRd

1.9828165 22 PRd

1.275131.9)( PQRP

Example 4Example 4

Draw a picture:

Define the variables:Width = w

Length = 3w

Width = w

Length = 3w

Perimeter of a rectangle:

wlP 22

w

ww

wwP

8

26

232

w

w

4

82Be sure to answer the question!Width = 4

Length = 3(4) = 12

HW: Page 49 (1 – 11 all; 13 – HW: Page 49 (1 – 11 all; 13 – 35 evens)35 evens)