1. Lesson 1 – 6 Two-Dimensional Figures
Geometry
Lesson 1 – 6
Two-Dimensional Figures
Objective:
Identify and name polygons.
Find perimeter, circumference, and area of two-dimensional figures.

2. 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.

3. Polygons

4. Not Polygons

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

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

7. Naming Polygons Triangle Octagon Quadrilateral Nonagon Pentagon
3 sides
4 sides
5 sides
6 sides
7 sides
8 sides
9 sides
10 sides
11 sides
12 sides
Triangle
Octagon
Quadrilateral
Nonagon
Pentagon
Decagon
Hexagon
Hendecagon
Heptagon
Dodecagon

8. 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.

9. Classify by sides, convex or concave, regular or irregular
Hexagon
Octagon
Concave
Convex
Irregular
Regular

10. Classify by sides, convex or concave, regular or irregular
Quadrilateral
Decagon
Hexagon
Concave
Convex
Convex
Irregular
Irregular
Regular
Look at this angle it is over
180 degrees Which is different
from marked angles.

11. Formulas Perimeter Circumference Area
The sum of the sides of a polygon
Circumference
Distance around a circle
Area
The number of square units needed to cover a surface.

12. Triangle
P – perimeter
A – area
b – base
h - height

13. Square

14. Rectangle

15. Circle
C – circumference
r – radius
d - diameter

16. Find the perimeter (circumference) and area.
= 10.6 cm
Have both
A = (3.2)(2.1)
= 6.72 cm2

17. Find the perimeter (circumference) and area.

18. 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.
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.

19. = 17.9 units Graph the points QR = 7 units (just count the squares)
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)
Add up sides to find perimeter
Use radical expression so answer is
Not rounded more than once.
= 17.9 units
Continued…

20. 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
= 14 units2

21. Homework
Pg – 10 all, 12 – 64 EOE