486 CHAPTER 8 Geometry 55. Area of a Basketball Court A National Basketball Association (NBA) basketball court is a rectangle that is 94 ft long and 50 ft wide. a) If you were to walk around the outside edge of a basketball court, how far would you walk? 288 ft b) If you had to place floor tiles that each measured 1 foot by 1 foot on a basketball court, how many tiles would you need? 4700 tiles 56. Pickleball A standard pickleball court is rectangular in shape and is 44 feet long by 20 feet wide. a) If you were to walk around the outside edge of a pickleball court, how far would you walk? 128 ft b) What is the area of one pickleball court? 880 ft2 c) Jimmy needs to paint the six courts at Lakewood Pickleball Club. One gallon of pickleball court paint covers 120 square feet. How many gallons will Jimmy need to paint all six courts? 44 gal 57. Countertops Melvin is the manager of an apartment building that has 18 apartments. Each apartment has three granite countertops that are rectangular and have the following dimensions: 3 ft 6 ft, 2 ft 8 ft, 1 2 1 2 × × and 3 ft 11 ft. 1 2 × Melvin must reseal each of the countertops in each apartment. Each bottle of sealant costs $19 and covers 60 square yards. Only whole bottles may be purchased. a) Determine the total area, in square feet, of all the countertops in all the apartments. 1359 ft2 b) Convert this area to square yards. 151 yd2 c) How many bottles of sealant will Melvin have to purchase? 3bottles d) What will be the cost of the sealant? $57 58. Football Field A football field is rectangular in shape and is 120 yards long by 53 yards wide. 1 3 To help improve wireless communications during games, a single wire antennae is being placed, underground, along the perimeter of the field. a) What is the length of the single wire antennae in yards? 346 yd 2 3 b) What is the length of the single wire antennae in feet? 1040 ft c) What is the area of the football field in square yards? 6400 yd2 d) What is the area of the football field in square feet? 57,600 ft2 Challenge Problems/Group Activities 59. Heron’s Formula A second formula for determining the area of a triangle (called Heron’s formula) is A s s a s b s c ( )( )( ) = − − − $ where s a b c ( ) 1 2 = + + and a b, , and c are the lengths of the sides of the triangle. Use Heron’s formula to determine the area of right triangle ABC and check your answer using the formula = A ab. 1 2 24 cm2 6 cm B 10 cm 8 cm C A 60. Expansion of a b ( )2 + In the figure, one side of the largest square has length a b. + Therefore, the area of the largest square is a b ( ) .2 + Answer the following questions to determine a formula for the expansion of a b ( ) .2 + a + b a + b a a b b 3 4 2 1 a) What is the area of the square marked ①? a2 b) What is the area of the rectangle marked ②? ab c) What is the area of the rectangle marked ③? ab d) What is the area of the square marked ④? b2 e) Add the four areas determined in parts (a) through (d) to write a formula for the expansion of a b ( ) .2 + a b a ab b ( ) 2 2 2 2 + = + + Recreational Mathematics 61. Sports Areas Research the official dimensions of the playing surface of your favorite sport. Determine the perimeter of the playing surface in both feet and yards and the area of the playing surface in both square feet and square yards. Answers will vary. 62. Scarecrow’s Error In the movie The Wizard of Oz, once the scarecrow gets his diploma he states the following: “In an isosceles triangle, the sum of the square roots of the two equal sides is equal to the square root of the third side.” Discuss why this statement is incorrect. Answers will vary.
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