polygons a closed figure formed by a finite number of coplanar segments such that: 1.the sides that...
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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.
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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.
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Special NamesSpecial NamesPolygons can be classified by the number
of sides they have:
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Regular PolygonRegular Polygon
VUWVUTPWQPRQSRTSUT
UVWPQRST
A convex polygon in which all sides are congruent and all angles are congruent
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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?
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PerimeterPerimeter
The sum of the lengths of the sides of a polygon.
Some polygons have “shortcut” formulas:
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Example 2Example 2
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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
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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
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HW: Page 49 (1 – 11 all; 13 – HW: Page 49 (1 – 11 all; 13 – 35 evens)35 evens)