Prentice Hall Geometry

Chapter 1 Tools of Geometry > 1-8 Perimeter, Circumference, and Area

The units of measurement for perimeter and circumference include inches, feet, yards, miles, centimeters, and meters. When measuring area, use square units such as square inches open , in. squared , close comma square feet open , ft squared , close comma square yards open , yd squared , close comma square miles open , mi squared , close comma square centimeters open , cm squared , close comma and square meters open , m squared , close .

Problem 1 Finding the Perimeter of a Rectangle

Landscaping The botany club members are designing a rectangular garden for the courtyard of your school. They plan to place edging on the outside of the path. How much edging material will they need?

A rectangular garden of length 22 feet and width 16 feet is surrounded by a path with width 4 feet.

Step 1 Find the dimensions of the garden, including the path.

For a rectangle, “length” and “width” are sometimes used in place of “base” and “height.”

Width of the garden and path

= 4 + 16 + 4 = 24 equals 4 plus 16 plus 4 equals 24

Length of the garden and path

= 4 + 22 + 4 = 30 equals 4 plus 22 plus 4 equals 30

Plan

Why should you draw a diagram?

A diagram can help you see the larger rectangle formed by the garden and the path, and which lengths to add together.
Step 2 Find the perimeter of the garden including the path.

P = 2 b + 2 h Use the formula for the perimeter of a rectangle. = 2 ( 24 ) + 2 ( 30 ) Substitute 24 for b and 30 for h . = 48 + 60 Simplify. = 108 table with 4 rows and 3 columns , row1 column 1 , p , column 2 equals 2 b plus 2 h , column 3 cap usetheformulafortheperimeterofarectangle. , row2 column 1 , , column 2 equals 2 open 24 close plus 2 open 30 close , column 3 cap substitute . 24 , for , b , and , 30 , for , h . , row3 column 1 , , column 2 equals 48 plus 60 , column 3 cap simplify. , row4 column 1 , , column 2 equals 108 , column 3 , end table

You will need 108 ft of edging material.

✓ Got It?

You want to frame a picture that is 5 in. by 7 in. with a 1-in.-wide frame.
1. What is the perimeter of the picture?
2. What is the perimeter of the outside edge of the frame?

You can name a circle with the symbol circle dot . For example, the circle with center A is written circle dot eh .

The formulas for a circle involve the special number p i open pi close . Pi is the ratio of any circle's circumference to its diameter. Since pi is an irrational number,

pi equals 3 . , 1415926 , dot dot dot comma

you cannot write it as a terminating decimal. For an approximate answer, you can use 3.14 or 22 over 7 for π. You can also use the begin circle , pi , end circle key on your calculator to get a rounded decimal for π. For an exact answer, leave the result in terms of π.

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Problem 1 Finding the Perimeter of a Rectangle

Plan

✓ Got It?

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