Chapter 9 Geometry © 2008 Pearson Addison-Wesley. All rights reserved

© 2008 Pearson Addison-Wesley. All rights reserved 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 Chapter 1 Section 9-3 Perimeter, Area, and Circumference

© 2008 Pearson Addison-Wesley. All rights reserved 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 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 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 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 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 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 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 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 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 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 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 Example: Area of a Parallelogram Find the area of the trapezoid below. Solution 13 cm. 5 cm. 7 cm.

© 2008 Pearson Addison-Wesley. All rights reserved 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 Example: Area With Multiple Shapes Find the area of the shaded region below. Solution Area of square – Area of triangle 4 in.

© 2008 Pearson Addison-Wesley. All rights reserved Circumference of a Circle The distance around a circle is called its circumference.

© 2008 Pearson Addison-Wesley. All rights reserved 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

© 2008 Pearson Addison-Wesley. All rights reserved Area of a Circle The area A of a circle with radius r is given by the formula. r

© 2008 Pearson Addison-Wesley. All rights reserved Example: Circle Find the area and circumference of a circle with a radius that is 6 inches long (use 3.14 as an approximation for pi). Solution Circumference Area