Geometry Lesson 1 6 TwoDimensional Figures Objective Identify

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. l Sides have a common endpoint and are noncollinear l Each side intersect exactly two other sides only at their endpoints Named l 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 5 sides Pentagon Octagon Nonagon 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 l. A polygon with all sides congruent Equiangular polygon l. A polygon with all angles congruent. Regular polygon l. A polygon that is BOTH equilateral and equiangular. Irregular l. 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 l The sum of the sides of a polygon Circumference l Distance around a circle Area l 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 cm 2 Have both

Find the perimeter (circumference) and area. P = 9. 5 + 10. 2 = 29. 2 in = 40. 8 in 2

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) Add up sides to find perimeter Use radical expression so answer is Not rounded more than once. = 17. 9 units Continued…

Continued… Find the Area of a triangle is A = (1/2)bh What is our base? 7 units What is our height? 4 units = 14 units 2

Homework Pg. 61 1 – 10 all, 12 – 64 EOE