482 CHAPTER 8 Geometry Square Unit Conversions fertilizer is determined by dividing the total area to be fertilized by the number of square feet covered per bag. The number of bags of fertilizer is 22,907.61 5000 , or about 4.58 bags. Therefore, Altay needs five bags. At $29.95 per bag, the total cost is 5 $29.95, × or $149.75. 7 Now try Exercise 53 Example 6 Converting Between Square Feet and Square Inches a) Convert 1 ft2 to square inches. b) Convert 37 ft2 to square inches. c) Convert 432 in.2 to square feet. Solution a) 1 ft 12 in. = Therefore, 1 ft 12 in. 12 in. 144 in. 2 2 = × = b) From part (a), we know that 1 ft 144 in. . 2 2 = Therefore, 37 ft 37 144 in. 5328 in. . 2 2 2 = × = c) In part (b), we converted from square feet to square inches by multiplying the number of square feet by 144. Now, to convert from square inches to square feet we will divide the number of square inches by 144. Therefore, 432 in. ft 3 ft . 2 432 144 2 2 = = 7 Now try Exercise 37 Example 7 Board Room Flooring Ursula wishes to purchase and have marble flooring installed in the board room at her company headquarters. The rectangular board room measures 33 ft 15 ft. × The cost of the flooring, including installation, is $245 per square yard. a) Determine the area of the board room floor in square yards. b) Determine the cost of the marble flooring for the board room. Solution a) The area of the floor, in square feet, is 33 ft 15 ft 495 ft .2 × = Since 1 yd 3 ft, 1 yd 3 ft 3 ft 9 ft . 2 2 = = × = To determine the area of the floor in square yards, we divide the area of the floor in square feet by 9 ft .2 Area in square yards 495 9 55 = = Therefore, the area of the board room floor is 55 yd .2 b) The cost of 55 yd2 of the marble flooring, including installation, is 55 $245 $13,475. ⋅ = 7 Now try Exercise 57 Exercises Warm Up Exercises In Exercises 1– 4, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. a) The sum of the lengths of the sides of a two-dimensional figure is called the _______ of the figure. Perimeter b) The measure of the region within the boundaries of a twodimensional figure is called the _______ of the figure. Area 2. In a right triangle, the side that is opposite the right angle is called the _______. Hypotenuse 3. A set of points equidistant from a fixed point is called a(n) _______. Circle 4. a) A line segment from the center of a circle to any point on the circle is called the _______ of the circle. Radius SECTION 8.3 Timely Tip When multiplying two lengths, be sure that the units of measure are the same. For example, in Example 7 you can multiply 33 feet by 15 feet to get 495 square feet. Or you can multiply 11 yards by 5 yards to get 55 square yards. However, you cannot get a valid answer if you multiply a length measured in feet by a length measured in yards. Instructor Resources for Section 8.3 in MyLab Math • Objective-Level Videos 8.3 • Interactive Concept Video: Applications Involving Areas of Circles • Interactive Concept Video: Applications Involving Circumference • Animation: Pythagorean Theorem • PowerPoint Lecture Slides 8.3 • MyLab Exercises and Assignments 8.3
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