Section 1.6: Two-Dimensional Figures by Shane McGinley

Polygons The term polygon is derived from a Greek word meaning many angles. A polygon is a closed figure formed by a finite number of coplanar segments called sides, such as: The sides that have a common endpoint are considered noncollinear. Each side intersects exactly two other sides, but only at their endpoints. The vertex of each angle is a polygon’s vertex. A polygon is named by the vertices’ letters, written in the order of consecutive vertices. A B C D Polygon ABCD Vertex C Side DA

Polygons (continued) The table below displays some examples of polygons and some that are not polygons. Polygons Not Polygons

Polygons (continued) A polygon can either be concave or convex. Assume that the line that contains each side of the polygon is drawn. If any of those lines contain a point on the inside of the polgyon, it is concave. Otherwise, it is convex. Convex Polygon Concave Polygon

Polygons (continued) Generally, a polygon is classified by the number of sides it has. The table below lists common names for various types of polygon. As you can see, a polygon having n sides is an n-gon. # of sides

Equilateral and Equiangular Polygons An equilateral polygon is a polygon in which all of its sides are congruent. An equiangular polygon is a polygon in which all of its angles are congruent. Equilateral Polygon Equiangular Polygon

Equilateral and Equiangular Polygons (continued) A convex polygon that is equilateral and equiangular is known as a regular polygon. An irregular polygon is a polygon that is not regular. V W XY Z regular polygon VWXYZ

Sample Problems Identify each polygon as either convex or concave. Explain. A. This polygon is convex, because none of the lines containing the sides of the polygon will pass through the interior of the hexagon. B. This polygon is concave, because two of the lines containing the sides of the polygon will pass through the interior of the Hexagon.

Practice Problems Identify each polygon as either convex or concave. Explain.

Perimeter, Circumference, and Area The perimeter of a polygon is the sum of the lengths of the polygon’s sides Some certain shapes have special formulas or perimeter, but every one is derived from the basic perimeter definition. The circumference of circle is distance around the circle.

Perimeter, Circumference, and Area (continued) The area of a figure is how many square units are needed to cover a certain surface. The table below shows the formulas for the perimeter and area of three common polygons and a circle. cd h bl w s s s s d r P-perimeter B-Base H-Height A-Area L-Length W-Width C-Circumference R-radius D-diameter

Sample Problems Find the perimeter or circumference and area of each figure A. 4.4 in 3.8 in P=b+c+d = (2) = =12.6 A=1/2bh =1/2(3.8)(4) =1/2(15.2) =7.6 4 in B. 4 cm C=2(3.14..)r =2(3.14..)(4) =25.1 A=(3.14..)r^2 =(3.14..)(4)^2 =50.3

Practice Problems Find the perimeter or circumference and area of each figure ft 5 ft 11 in

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