Geometry
Lesson 1 – 6
Two-Dimensional Figures
Objective:
Identify and name polygons.
Find perimeter, circumference, and area of two-dimensional figures.
Polygon
A closed figure formed by a finite
number of coplanar segments called
sides.
 Sides
have a common endpoint and are
noncollinear
 Each side intersect exactly two other
sides only at their endpoints
Named
 Named
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 Polygons
3 sides Triangle
8 sides
4 sides Quadrilateral 9 sides
Octagon
Nonagon
5 sides Pentagon
10 sides Decagon
6 sides Hexagon
11 sides Hendecagon
7 sides Heptagon
12 sides Dodecagon
Definitions
n-gon: a polygon with n sides
Equilateral polygon
A
polygon with all sides congruent
Equiangular polygon
A
polygon with all angles congruent.
Regular polygon
A
polygon that is BOTH equilateral and
equiangular.
Irregular
A
polygon that is not regular.
Classify by sides, convex or
concave, regular or irregular
Hexagon
Concave
Irregular
Octagon
Convex
Regular
Classify by sides, convex or
concave, regular or irregular
Quadrilateral
Decagon
Hexagon
Convex
Irregular
Concave
Convex
Regular
Irregular
Look at this angle it is over
180 degrees Which is different
from marked angles.
Formulas
Perimeter
 The
sum of the sides of a polygon
Circumference
 Distance
around a circle
Area
 The
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
C  2 (3)
 6 in
 18.85 in
A   (3)
Have both
2
 9  28.27 in
2
Find the perimeter
(circumference) and area.
C   (6.2)
 6.2 cm
 19.48 cm
P = 9.5 + 9.5 + 10.2
= 29.2 in
A   3.1
2
 9.61 cm
2
 30.19 cm
2
1
A  10.2 8
2
= 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.
B.
C.
D.
Right triangle with each leg about 7 cm long
Circle with radius of about 4 cm long
Rectangle with a length of 8 cm and a width of
4.5 cm
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 points
Find the distance of each side to find Perimeter
QR = 7 units (just count the squares)
QP 
 1  3  3  1
2
2
 4  16
Add up sides to find perimeter
Use radical expression so answer is
Not rounded more than once.
 20
 2 5 units
PR 
 1  4  3  1
2
 25  16
 41 units
2
P  7  2 5  41
= 17.9 units
Continued…
Continued… Find the Area
Area of a triangle is A = (1/2)bh
What is our base? 7 units
What is our height? 4 units
1
A  7 4 
2
= 14 units2
Homework
Pg. 61 1 – 10 all, 12 – 64 EOE