Objectives Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More with Formulas 1. Use the formula P = 2l + 2w to find the perimeter of a rectangle. 2. Use the formula A = bh to find the area of a parallelogram. 3. Use the formula V= lwh to find the volume of a box. 4. Solve for an unknown number in a formula. 5. Use a problem solving process to solve problems requiring more than one formula 1.6

Slide 2 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 1 Use the formula P = 2l + 2w to find the perimeter of a rectangle.

First, lets derive a formula for the perimeter of a rectangle. Look at the rectangle below. We use the variable l to represent length and w for width. Slide 3 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Perimeter of a rectangle = length + width + length + width ww l l

Slide 4 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1.Replace the variables with the corresponding known values. 2.Solve for the unknown variable. Procedure

Slide 5 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 1 A school practice field is to be enclosed with a chain-link fence. The field is 400 feet long by 280 feet wide. How much fencing is needed? Solution: 280 ft. 400 ft.

Slide 6 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 2 Use the formula A = bh to find the area of a parallelogram.

Slide 7 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definition Parallel lines: Straight lines lying in the same plane that do not intersect. Parallelogram: A four sided figure with two pairs of parallel lines. Rectangles are special forms of a more general class of figures called parallelograms, which have two pairs of parallel lines.

Examples of parallelograms: Slide 8 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To find the area of a parallelogram, we need the measure of the base and height. The height is measured along a line that makes a 90º angle with the base. An angle that measures 90º is called a right angle.

Slide 9 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definition Right angle: An angle that measure 90º. We will use the letter b for the measure of the base and h for the height. h b Note: The right angle is indicated by a small square where the height line meets the base.

If we slide that triangle around to the right side and place the parallel sides together, the resulting figure is a rectangle. Slide 10 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Notice that if we cut along the height line we would cut off a triangle. The rectangle has the same area as the original parallelogram. The length of this rectangle is b and the width is h. So the formula to calculate the area of a parallelogram is… A = bh h b

Slide 11 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 2 Find the area of the parallelogram. Solution: We use the formula for the area of a parallelogram. Answer: A = bh 9 ft. 15 ft.

Slide 12 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 3 Use the formula V = lwh to find the volume of a box.

Slide 13 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definition Cubic unit: A 1 x 1 cube. Volume: The total number of cubic units that completely fill an object. Examples of cubic units… Cubic centimeter 1 cm Cubic inch 1 in.

Slide 14 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 3 A computer tower is 30 centimeters long by 10 centimeters wide by 35 centimeters high. What is the volume of the tower? Solution: Because the tower is a box, we use the formula for the volume of a box.

Slide 15 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 4 Solve for an unknown number in a formula.

Slide 16 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 4 The area of a parallelogram is 40 square feet. If the base is 8 feet, find the height. Solution: Use the formula A = bh.

Slide 17 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 5 The volume of a box is 480 cubic centimeters. If the length is 10 centimeters and the width is 8 centimeters, find the height. Solution: Use the formula V = lwh.

Slide 18 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 5 Use a problem-solving process to solve problems requiring more than one formula.

Slide 19 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Problem-Solving Outline. Procedure 1.Understand the problem. a.Read the question(s) (not the whole problem, just the question at the end) and note what it is you are to find. b.Now read the whole problem, underlining the key words. c.If possible and useful, draw a picture, make a list or table, simulate the situation, or search for a related example problem.

Slide 20 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Problem-Solving Outline. Procedure 2.Plan your solution strategy by searching for a formula or translating the key words to an equation. 3.Execute the plan by solving the formula or equation. 4.Answer the question. Look at your note about what you were to find and make sure you answered that question. Include appropriate units.

Slide 21 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Problem-Solving Outline. Procedure 5.Check the results. a.Try finding the solution in a different way, revising the process, or estimating the answer and making sure the estimate and actual answer are reasonably close. b.Make sure the answer is reasonable.

Slide 22 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 6 Crown molding is to be installed in a room that is 20 feet long by 15 feet wide. The type of molding desired costs $6 per foot to install. How much will it cost to install the molding? 15 ft. 20 ft.

Understand: We are to find the total area occupied by the building. Slide 23 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 7 Shown here is a base plan for a new building. What is the total area occupied by the building? 60 ft. 90 ft. 40 ft. 50 ft.

Slide 24 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 8 A builder is required to sod the yard of a new home. The lot is a rectangle 75 feet wide by 125 feet long. The house occupies 2500 square feet of the lot. Sod must be purchased in pallets of 500 square feet that costs $85 each. How much will it cost to sod the yard?