GeometryLesson 1 – 6

Two-Dimensional Figures

Objective:Identify and name polygons.

Find perimeter, circumference, and area of two-dimensional figures.

PolygonA closed figure formed by a finite number of coplanar segments called sides.Sides have a common endpoint and are

noncollinearEach side intersect exactly two other

sides only at their endpoints

NamedNamed using the vertexes in order

around the polygon.

Polygons

Not Polygons

Concave

When the sides (or diagonals) of the figure are extended (or drawn) at least one intersects the interior of the figure.

Convex

When the sides (or diagonals) of the figure are extended (or drawn) they do not intersect the interior of the figure.

Naming Polygons3 sides

4 sides

5 sides

6 sides

7 sides

8 sides

9 sides

10 sides

11 sides

12 sides

Triangle Octagon

Quadrilateral

Pentagon

Hexagon

Heptagon

Nonagon

Decagon

Hendecagon

Dodecagon

Definitionsn-gon: a polygon with n sidesEquilateral polygonA polygon with all sides congruent

Equiangular polygonA polygon with all angles congruent.

Regular polygonA polygon that is BOTH equilateral and

equiangular.

IrregularA polygon that is not regular.

Classify by sides, convex or concave, regular or irregular

HexagonConcaveIrregular

OctagonConvexRegular

Classify by sides, convex or concave, regular or irregular

Quadrilateral

Convex

Irregular

Decagon

Concave

Irregular

Hexagon

Convex

RegularLook at this angle it is over 180 degrees Which is different from marked angles.

Formulas

PerimeterThe sum of the sides of a polygon

CircumferenceDistance around a circle

AreaThe number of square units needed

to cover a surface.

Triangle

P – perimeter

A – area

b – base

h - height

Square

Rectangle

Circle

C – circumference

r – radius

d - diameter

Find the perimeter (circumference) and area.

P = 2(3.2) + 2(2.1)

= 10.6 cm

A = (3.2)(2.1)

= 6.72 cm2

)3(2Cin6in85.18

Have both

2)3(A227.289 in

Find the perimeter (circumference) and area.

)2.6(C

cm

cm

48.19

2.6

21.3A

2

2

19.30

61.9

cm

cm

P = 9.5 + 9.5 + 10.2= 29.2 in

82.102

1A

= 40.8 in2

Standardized Test Practice

Yolanda has 26 cm of cording to frame a photograph in her scrapbook. Which of these shapes would use most or all of the cording and enclose the largest area.

A. Right triangle with each leg about 7 cm longB. Circle with radius of about 4 cm longC. Rectangle with a length of 8 cm and a width of

4.5 cmD. Square with a side length of 6 cm.

*Hint which one has a perimeter close to 26 and the highest area.

Find the perimeter and area of triangle PQR with vertices P(-1,3), Q(-3,-1), and R(4, -1).

Graph the pointsFind the distance of each side to find Perimeter

QR = 7 units (just count the squares)

units

QP

52

20

164

1331 22

units

PR

41

1625

1341 22

Add up sides to find perimeterUse radical expression so answer is Not rounded more than once.

41527 P= 17.9 units

Continued…

Continued… Find the Area Area of a triangle is A = (1/2)bh

What is our base?

What is our height?

7 units

4 units

472

1A

= 14 units2

Homework

Pg. 61 1 – 10 all, 12 – 64 EOE