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© 2008 Pearson Addison-Wesley. All rights reserved 9-3-2 Chapter 9: Geometry 9.1 Points, Lines, Planes, and Angles 9.2 Curves, Polygons, and Circles 9.3 Perimeter, Area, and Circumference 9.4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem 9.5Space Figures, Volume, and Surface Area 9.6Transformational Geometry 9.7 Non-Euclidean Geometry, Topology, and Networks 9.8 Chaos and Fractal Geometry

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-4 Perimeter, Area, and Circumference Perimeter of a Polygon Area of a Polygon Circumference of a Circle Area of a Circle

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-5 Perimeter of a Polygon The perimeter of any polygon is the sum of the measures of the line segments that form its sides. Perimeter is measured in linear units.

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-6 Perimeter of a Triangle a b c The perimeter P of a triangle with sides of lengths a, b, and c is given by the formula P = a + b + c.

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-7 Perimeter of a Rectangle The perimeter P of a rectangle with length l and width w is given by the formula P = 2l + 2w, or equivalently P = 2(l + w). w l

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-8 Perimeter of a Square The perimeter P of a square with all sides of length s is given by the formula P = 4s. s s

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-9 Area of a Polygon The amount of plane surface covered by a polygon is called its area. Area is measured in square units.

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-10 Area of a Rectangle The area A of a rectangle with length l and width w is given by the formula A = lw. w l

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-11 Example: Rectangle Find the perimeter and area of the rectangle below. 7 ft. 15 ft. Solution P = 2l + 2w = 2(15) + 2(7) = 44 ft. Perimeter Area A = lw = 15(7) = 105 ft. 2

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-12 Area of a Square The area A of a square with all sides of length s is given by the formula P = s 2. s s

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-13 Area of a Parallelogram The area A of a parallelogram with height h and base b is given by the formula A = bh. b h

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-14 Area of a Trapezoid The area A of a trapezoid with parallel bases b and B and height h is given by the formula B h b

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-16 Area of a Triangle The area A of a triangle with base b and height h is given by the formula h b

© 2008 Pearson Addison-Wesley. All rights reserved 9-3-19 Circumference of a Circle The circumference C of a circle of diameter d is given by the formula. or equivalently where r is a radius. d r