Definition/Procedure Example Surface Area of a Rectangular Solid The surface area of a three-dimensional object is the total area on the surface of the object. The surface area, SA, of a rectangular solid with length l, width w, and height h is SA 2lw 2lh 2wh Because we are fi nding the total area on the surface of the object, surface area is measured in square units. (p. 322) Find the surface area of this box. 5 ft 3 ft 2 ft Identify the length, width, and height, then substitute them into the formula. l 5 ft, w 3 ft, h 2 ft SA 2lw 2lh 2wh SA 2(5 ft)(3 ft) 2(5 ft)(2 ft) 2(3 ft)(2 ft) SA 30 ft2 20 ft2 12 ft2 SA 62 ft2 4.5 Solving Geometry Applications Using Algebra We can use geometry formulas to solve for unknown values. (p. 333) The formula for the area of a triangle is A 1 2 bh. If A 72 cm when b 16 cm, fi nd the height, h. A 1 2 bh 72 1 2 (16)h Substitute the given values. 72 8h Multiply. 72 8 8h 8 Divide both sides by 8. 9 h Simplify. To solve some applications, we can use the fi ve-step process to write an equation and solve. (p. 334) A rectangular piece of poster board is 6 in. longer than it is wide. If its perimeter is 132 in., fi nd its dimensions. Step 1: Read the problem carefully, and identify what we are being asked to fi nd. We must fi nd the length and width of the poster board. Draw a picture. w w 1 6 Step 2: Choose a variable to represent the unknown, and defi ne the other unknown in terms of this variable. w the width of the poster board w 6 the length of the poster board Label the picture with the expressions for the width and length. 348 CHAPTER 4 Basic Geometry Concepts and Algebra www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
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