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Geometry

Learn about polygons, their classification, and how to find their perimeter and area using formulas. Also, practice solving standardized test questions and complete homework exercises.

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Geometry

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  1. 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. 3 sides 4 sides 5 sides 6 sides 7 sides 8 sides 9 sides 10 sides 11 sides 12 sides Naming Polygons 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 • 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. P = 2(3.2) + 2(2.1) = 10.6 cm Have both A = (3.2)(2.1) = 6.72 cm2

  17. Find the perimeter (circumference) and area. P = 9.5 + 9.5 + 10.2 = 29.2 in = 40.8 in2

  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. 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. 61 1 – 10 all, 12 – 64 EOE

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