GEOMETRYSection 1.6

Two-Dimensional Figures

POLYGONS Derived from a Greek word meaning

“many sides”. Polygon- closed figure formed by a

finite number of coplanar segments called sides such that:The sides that have a common endpoint are noncollinear

Each side intersects exactly two other sides

Vertex of the polygon- vertex of each angle

Polygons are classified by the number of sides.

3-Triangle, 9-Nonagon 4-Quadrilateral, 10-Decagon

5-Pentagon,11- Hendecagon

6-Hexagon, 12-Dodecagon

7-Heptagon 8-Octagon

Polygons are named by the letters of its consecutive (in order) vertices.

Concave- some lines (when extended) pass through the interior of the polygon

Convex- no points of the lines (when extended) are in the interior.

Equilateral polygon - all sides are congruent.

Equiangular polygon - all angles are congruent.

Regular polygon - convex, equilateral, and equiangular.

Irregular – everything else

EXAMPLE 1 Name each polygon by its

number of sides, then state whether it is convex or concave, regular or irregular.

Perimeter - sum of the lengths of all the sidesUnits stay the same.

Circumference -distance around a circleUnits stay the same.

Area - number of square units needed to cover a surfaceUnits are squared.

FORMULASTriangle Square Rectangl

eCircle

Perimeter P = b + c

+dP = 4s P=2l

+2wC= πd

Area A= 1/2bh A=s2 A=lw A=πr2

THE PYTHAGOREAN THEOREM For any right triangle,

EXAMPLE 3 Find the area and perimeter (or

circumference) of each figure.

12.4ft

18.9ft

5cm

12cm

6m

EXAMPLE 4 What is the perimeter of a

rectangle if its length is half its width and its area is 48 in2?

HOMEWORK Page 61: 1-10 all, 12- 26 evens,

32-42 evens