Post on 29-Dec-2015
8-3 Perimeter and Circumference
Course 2
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Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
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1. 6.78 kilograms = ________grams
2. 2345 cm = _________meters
3. 27,360 inchs + 8280 ft = _______miles
Course 2
8-3 Perimeter and Circumference
Problem of the Day
A rectangular piece of sheet metal measures 5 in. by 6 in. A rectangular notch 1 in. deep and in. wide is cut
Course 2
8-3 Perimeter and Circumference
764
out of the middle of each side. What isthe perimeter of the piece after the cuts have been made? (Hint: You don’t have to use fractions.)30 in. (the original 6 in. by 5 in. sheet plus 8 in. for the eight 1 in. cuts)
Learn to find the perimeter of a polygon and the circumference of a circle.
Course 2
8-3 Perimeter and Circumference
Course 2
8-3 Perimeter and Circumference
The distance around a geometric figure is its perimeter. To find the perimeter P of a polygon, you can add the lengths of its sides.
Find the perimeter.
Additional Example 1: Finding the Perimeter of a Polygon
Course 2
8-3 Perimeter and Circumference
25 cm25 cm
15 cm
P = 25 + 25 + 15 Use the side lengths.
P = 65
The perimeter of the triangle is 65 cm.
Add.
Check It Out: Example 1
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Course 2
8-3 Perimeter and Circumference
20 cm25 cm
30 cm
P = 25 + 20 + 30 Use the side lengths.
P = 75
The perimeter of the triangle is 75 cm.
Add.
Find the perimeter of the polygon.
Course 2
8-3 Perimeter and Circumference
The perimeter P of a rectangle is the sum of twice its length l and twice its width w.
w
l
PERIMETER OF A RECTANGLE
P = 2l + 2w
Find the perimeter of a rectangle.
Additional Example 2: Using Properties of a Rectangle to Find Perimeter
Course 2
8-3 Perimeter and Circumference
14 ft
18 ft
P = 2l + 2wP = (2 · 18) + (2 ·14)P = 36 + 28P = 64
The perimeter of the rectangle is 64 ft.
Use the formula.Substitute for l and w.Multiply.Add.
Check It Out: Example 2
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Course 2
8-3 Perimeter and Circumference
Find the perimeter of a rectangle.
16 ft
8 ft
P = 2l + 2wP = (2 · 8) + (2 · 16)P = 16 + 32P = 48
The perimeter of the rectangle is 48 ft.
Use the formula.Substitute for l and w.Multiply.Add.
Course 2
8-3 Perimeter and Circumference
Cd
The distance around a circle is called circumference. For every circle, the ratio of circumference C to diameter d is the same. This ratio, , is
represented by the Greek letter , called pi. Pi is approximately equal to 3.14 or . By solving the 22
7equation = for C, you get the formula for circumference. the formula for circumference.C = d, or C = 2r.
Cd
Course 2
8-3 Perimeter and Circumference
Radius
Diameter
Circumference
C = d, or C = 2r
CIRCUMFERENCE OF A CIRCLE
The circumference C of a circle is times the diameter d, or 2 times the radius r.
Find the circumference of the circle to the nearest tenth. Use 3.14 for .
Additional Example 3A: Finding the Circumference of a Circle
12 in.C = d
C 3.14 · 12
C 37.68
You know the diameter.
Substitute for and d.
Multiply.
The circumference of the circle is about 37.7 in.
Course 2
8-3 Perimeter and Circumference
Find the circumference of the circle to the nearest tenth. Use 3.14 for .
Additional Example 3B: Finding the Circumference of a Circle
18 cmC = 2r
C 2 · 3.14 · 18
C 113.04
You know the radius.
Substitute for and r.
Multiply.
The circumference of the circle is about 113.0 cm.
Course 2
8-3 Perimeter and Circumference
Find the circumference of the circle to the nearest tenth. Use 3.14 for .
Check It Out: Example 3A
7 in.C = d
C 3.14 · 7
C 21.98
You know the diameter.
Substitute for and d.
Multiply.
The circumference of the circle is about 22.0 in.
Course 2
8-3 Perimeter and Circumference
Find the circumference of the circle to the nearest tenth. Use 3.14 for .
Check It Out: Example 3B
11 cmC = 2r
C 2 · 3.14 · 11
C 69.08
You know the radius.
Substitute for and r.
Multiply.
The circumference of the circle is about 69.1 cm.
Course 2
8-3 Perimeter and Circumference
Course 2
8-3 Perimeter and Circumference
If the diameter or radius of a circle is a
multiple of 7, use for .
Helpful Hint
22 7
The diameter of a circular pond is 42 m. What is its circumference? Use
Additional Example 4: Application
Course 2
8-3 Perimeter and Circumference
227
for .
C = d You know the diameter.
C 227
· 42 Substitute 227
for and 42 for d.
C 227
· 421
C 227
· 421
6
1C 132
The circumference of the pond is about 132 m.
Write 42 as a fraction.
Simplify.
Multiply.
The diameter of a circular spa is 14 m. What is its circumference? Use
Check It Out: Example 4
Course 2
8-3 Perimeter and Circumference
227
for .
C = d You know the diameter.
C 227
· 14 Substitute 227
for and 14 for d.
C 227
· 141
C 227
· 141
2
1C 44
The circumference of the spa is about 44 m.
Write 14 as a fraction.
Simplify.
Multiply.
Lesson QuizFind the perimeter.
1. 2.
3. What is the circumference of a circle with a a radius of 8 inches? Use 3.14 for . 4. If a guardrail is to be placed around the edge of a circular swimming pool with a diameter of 21 ft, how many feet of railing will be needed?
36 in.45 m
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50.24 in.
66 ft
Course 2
8-3 Perimeter and Circumference
8 m12 m
9 m6 m
10 m 8 in.
10 in.
227
Use for .