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

2. 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. 9.3-2

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

4. 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. 9.3-4

5. 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 = 330 270 = 89,100 ft 2 9.3-5

6. 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. 9.3-6

7. 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 $34,650. 9.3-7

8. 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

9. 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

10. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 2: Crossing a Moat Solution The ladder needs to be at least 30 ft long. 9.3-10

11. 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 9.3-11

12. 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 9.3-12

13. 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. 9.3-13

14. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Determining the Shaded Area Solution Height of parallelogram is diameter of circle: 4 ft 9.3-14

15. 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 ≈ 12.57 ft 2 9.3-15

16. 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 – 12.57 Area of shaded region ≈ 27.43 ft 2 9.3-16