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Transcript of Geometry
Geometry
9-3-2
Chapter 1
Topics: Perimeter, Area, and Circumference
9-3-3
Perimeter, Area, and Circumference
• Perimeter of a Polygon• Area of a Polygon • Circumference of a Circle• Area of a Circle
9-3-4
Perimeter of a Polygon
The perimeter of any polygon is the sum of the measures of the line segments that form its sides. Perimeter is measured in linear units.
© 2008 Pearson Addison-Wesley. All rights reserved9-3-5
Perimeter of a Triangle
ab
c
The perimeter P of a triangle with sides of lengths a, b, and c is given by the formula
P = a + b + c.
© 2008 Pearson Addison-Wesley. All rights reserved9-3-6
Perimeter of a Rectangle
The perimeter P of a rectangle with length l and width w is given by the formula
P = 2l + 2w,
or equivalently
P = 2(l + w).
w
l
9-3-7
Perimeter of a Square
The perimeter P of a square with all sides of length s is given by the formula
P = 4s.s
s
© 2008 Pearson Addison-Wesley. All rights reserved9-3-8
Area of a Polygon
The amount of plane surface covered by a polygon is called its area. Area is measured in square units.
© 2008 Pearson Addison-Wesley. All rights reserved9-3-9
Area of a Rectangle
The area A of a rectangle with length l and width w is given by the formula
A = lw.
w
l
9-3-10
Example: Rectangle
Find the perimeter and area of the rectangle below.
7 ft.
15 ft.
Solution
P = 2l + 2w = 2(15) + 2(7) = 44 ft.
Perimeter
Area
A = lw = 15(7) = 105 ft.2
© 2008 Pearson Addison-Wesley. All rights reserved9-3-11
Area of a Square
The area A of a square with all sides of length s is given by the formula
P = s2.s
s
© 2008 Pearson Addison-Wesley. All rights reserved9-3-12
Area of a Parallelogram
The area A of a parallelogram with height h and base b is given by the formula
A = bh.
b
h
© 2008 Pearson Addison-Wesley. All rights reserved9-3-13
Area of a Trapezoid
The area A of a trapezoid with parallel bases b and B and height h is given by the formula
B
h
b 1 .
2A h B b
© 2008 Pearson Addison-Wesley. All rights reserved9-3-14
Example: Area of a Parallelogram
Find the area of the trapezoid below.
Solution13 cm.
5 cm.
7 cm.
1 1 (5) 7 132 2
A h B b
21 (5) 20 50 cm.2
© 2008 Pearson Addison-Wesley. All rights reserved9-3-15
Area of a Triangle
The area A of a triangle with base b and height h is given by the formula
h
b
1 .2
A hb
© 2008 Pearson Addison-Wesley. All rights reserved9-3-16
Example: Area With Multiple Shapes
Find the area of the shaded region below.
SolutionArea of square – Area of triangle
2 12
s bh
4 in.
4 in.
2 214 (4)(4) 16 8 8 in.2
© 2008 Pearson Addison-Wesley. All rights reserved9-3-17
Circumference of a Circle
The distance around a circle is called its circumference.
© 2008 Pearson Addison-Wesley. All rights reserved9-3-18
Circumference of a Circle
The circumference C of a circle of diameter d is given by the formula.
or equivalently
where r is a radius.
,C d
2 ,C r d r
© 2008 Pearson Addison-Wesley. All rights reserved9-3-19
Area of a Circle
The area A of a circle with radius r is given by the formula.
2.A rr
© 2008 Pearson Addison-Wesley. All rights reserved9-3-20
Example: Circle
Find the area and circumference of a circle with a radius that is 6 inches long (use 3.14 as an approximation for pi).
Solution
2 2 (6) 12 37.68 in.C r Circumference
Area2 2 2(6) 36 113.04 in.A r