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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