Introduction to Perimeter, 1.7 Circumference, and Area
GOAL 1 REVIEWING PERIMETER, CIRCUMFERENCE, AND AREA What you should learn GOAL 1 Find the perimeter In this lesson, you will review some common formulas for perimeter, and area of common plane circumference, and area. You will learn more about area in Chapters 6, 11, and 12. figures. GOAL 2 Use a general problem-solving plan. PERIMETER, CIRCUMFERENCE, AND AREA FORMULAS Why you should learn it Formulas for the perimeter P, area A, and circumference C of some To solve real-life common plane figures are given below. problems about perimeter SQUARE RECTANGLE and area, such as finding the side length s length ¬ and width w number of bags of seed you L P = 4s P = 2¬ +2w need for a field in Example 4. A = s 2 A = ¬w s w
TRIANGLE CIRCLE side lengths a, b, radius r r a h c and c, base b, and C =2πr height h A =πr 2 b P = a + b + c Pi (π) is the ratio of the circle’s A = 1 bh circumference to its diameter. 2
The measurements of perimeter and circumference use units such as centimeters, meters, kilometers, inches, feet, yards, and miles. The measurements of area use units such as square centimeters (cm2), square meters (m2), and so on.
EXAMPLE 1 Finding the Perimeter and Area of a Rectangle
Find the perimeter and area of a rectangle of length 12 inches and width 5 inches.
SOLUTION Begin by drawing a diagram and labeling the length and width. Then, use the formulas for perimeter and area of a rectangle. 5 in. l l P = 2 + 2wA =w 12 in. = 2(12) + 2(5) = (12)(5) = 34 = 60 So, the perimeter is 34 inches and the area is 60 square inches.
1.7 Introduction to Perimeter, Circumference, and Area 51 EXAMPLE 2 Finding the Area and Circumference of a Circle
Find the diameter, radius, circumference, and area of the circle shown at the right. Use 3.14 as an approximation for π.
STUDENT HELP SOLUTION Study Tip From the diagram, you can see that the Some approximations for diameter of the circle is π = 3.141592654 . . . are 3.14 and 22 . d = 13 º 5 = 8 cm. 7 The radius is one half the diameter. d r = 1 (8) = 4 cm 2 Using the formulas for circumference and area, you have C = 2πr ≈ 2(3.14)(4) ≈ 25.1 cm A = πr2 ≈ 3.14(42) ≈ 50.2 cm2.
EXAMPLE 3 Finding Measurements of a Triangle in a Coordinate Plane
Find the area and perimeter of the triangle defined by D(1, 3), E(8, 3), and F(4, 7).
SOLUTION Plot the points in a coordinate plane. Draw y Æ F(4, 7) the height from F to side DE. Label the Æ point where the height meets DE as G. Point G has coordinates (4, 3).
base: DE = 8 º 1 = 7 D(1, 3) G(4, 3) E(8, 3)
height: FG = 7 º 3 = 4 1 A = 1 (base)(height) 1 x 2
= 1 (7)(4) 2 = 14 square units To find the perimeter, use the Distance Formula. STUDENT HELP 2 2 2 2 Skills Review EF = (4 º 8) + (7 º 3) DF = (4 º 1) + (7 º 3) For help with simplifying 2 2 2 2 radicals, see page 799. = (º4) + 4 = 3 + 4 = 3 2 = 2 5 = 4 2 units = 5 units