Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 9.3 Perimeter and Area

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Definitions The perimeter, P, of a two-dimensional figure is the sum of the lengths of the sides of the figure. The area, A, is the region within the boundaries of the figure

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Formulas 9.3-3

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 1: Sodding a Lacrosse Field Rob Marshall wishes to replace the grass (sod) on a lacrosse field. One pallet of Bethel Farms sod costs $175 and covers 450 square feet. If the area to be covered is a rectangle with a length of 330 feet and a width of 270 feet, determine a) The area to be covered with sod

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 1: Sodding a Lacrosse Field a) the area to be covered with sod. Solution A = l w = = 89,100 ft

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 1: Sodding a Lacrosse Field b)Determine how many pallets of sod Rob needs to purchase. Solution Rob needs 198 pallets of sod

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 1: Sodding a Lacrosse Field c)Determine the cost of the sod purchased. Solution The cost of 198 pallets of sod is 198 × $175, or $34,

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Pythagorean Theorem The sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse. leg 2 + leg 2 = hypotenuse 2 Symbolically, if a and b represent the lengths of the legs and c represents the length of the hypotenuse (the side opposite the right angle), then a 2 + b 2 = c 2 a b c 9.3-8

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 2: Crossing a Moat The moat surrounding a castle is 18 ft wide and the wall by the moat of the castle is 24 ft high (see Figure). If an invading army wishes to use a ladder to cross the moat and reach the top of the wall, how long must the ladder be? 9.3-9

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 2: Crossing a Moat Solution The ladder needs to be at least 30 ft long

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Circles A circle is a set of points equidistant from a fixed point called the center. A radius, r, of a circle is a line segment from the center of the circle to any point on the circle. A diameter, d, of a circle is a line segment through the center of the circle with both end points on the circle. d r circumference

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Circles The circumference is the length of the simple closed curve that forms the circle. d r circumference

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Determining the Shaded Area Determine the shaded area. Use the π key on your calculator and round your answer to the nearest hundredth

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Determining the Shaded Area Solution Height of parallelogram is diameter of circle: 4 ft

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Determining the Shaded Area Solution Area of parallelogram = bh = 10 4 = 40 ft 2 Area of circle = π r 2 = π (2) 2 = 4 π ≈ ft

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Determining the Shaded Area Solution Area of shaded region = Area of parallelogram – Area of circle Area of shaded region ≈ 40 – Area of shaded region ≈ ft