478 CHAPTER 8 Geometry Parallelogram Trapezoid w h b s2 s1 b2 b1 h P b w A bh 2 2 = + = P s s b b A h b b ( ) 1 2 1 2 1 2 1 2 = + + + = + Example 1 Office Flooring Malik wishes to install mahogany hardwood flooring in his home office. The rectangular office floor measures 18.5 feet by 12.5 feet. The flooring is sold in cartons that cost $220, and each carton contains 20 square feet of flooring. Only whole cartons of flooring may be purchased. a) Determine the area of the office floor. b) Determine the number of cartons of flooring Malik will need to purchase. c) Determine the cost of the flooring purchased. Solution a) The area of the office floor is A l w (18.5 ft)(12.5 ft) 231.25 ft2 = ⋅ = = The area is measured in square feet (ft2 ) because both length and width are measured in feet. b) To determine the number of cartons of flooring Malik needs, divide the area of the office floor, 231.25 ft ,2 by the area of flooring in one carton, 20 ft .2 Area of office floor Area of flooring in one carton 231.25 ft 20 ft 11.5625 2 2 = = Since only whole cartons are sold, Malik needs to purchase 12 cartons of flooring. c) Malik needs 12 cartons of flooring, and each carton costs $220; therefore, the cost of the flooring is 12 $220, ⋅ or $2640. 7 Now try Exercise 41 Did You Know? Pythagorean Theorem The Pythagorean theorem is one of the most famous theorems of all time. One book, Pythagorean Propositions , contains 370 different proofs of the Pythagorean theorem. U.S. President James A. Garfield gave one notable proof. The Pythagorean theorem has found its way into popular culture as well. In the movie The Wizard of Oz , the scarecrow incorrectly recites the Pythagorean theorem once the wizard grants him his diploma (see Exercise 62). In the play The Pirates of Penzance , the Major General refers to the Pythagorean theorem when he sings, “I’m teeming with a lot o’ news, with many cheerful facts about the square of the hypotenuse.” Lewis Carroll, author of Through the Looking Glass and Alice’s Adventures in Wonderland , stated that the Pythagorean theorem “is as dazzlingly beautiful now as it was in the day when Pythagoras discovered it.” Actually, the Pythagorean theorem was known to the ancient Babylonians in about 1600 B.C. , 1000 years before Pythagoras, and it continues to play a huge role in mathematics. Pictorial Press Ltd/Alamy Stock Photo Pythagorean Theorem We introduced the Pythagorean theorem in Chapter 5. Because this theorem is an important tool for determining the perimeter and area of triangles, we restate it here. 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 leg hypotenuse 2 2 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 b c 2 2 2 b c a Pythagorean Theorem
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