Geometry
Chapter 1
Topics: Perimeter, Area, and Circumference
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Perimeter, Area, and Circumference • • • •
Perimeter of a Polygon Area of a Polygon Circumference of a Circle Area of a Circle
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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.
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Perimeter of a Triangle The perimeter P of a triangle with sides of lengths a, b, and c is given by the formula P = a + b + c.
b
a c
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Perimeter of a Rectangle The perimeter P of a rectangle with length l and width w is given by the formula l P = 2l + 2w, w or equivalently P = 2(l + w).
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Perimeter of a Square The perimeter P of a square with all sides of length s is given by the formula s P = 4s. s
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Area of a Polygon The amount of plane surface covered by a polygon is called its area. Area is measured in square units.
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Area of a Rectangle The area A of a rectangle with length l and width w is given by the formula l A = lw. w
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Example: Rectangle Find the perimeter and area of the rectangle below. 15 ft.
Solution
7 ft.
Perimeter P = 2l + 2w = 2(15) + 2(7) = 44 ft. Area A = lw = 15(7) = 105 ft.2 9-3-10
Area of a Square The area A of a square with all sides of length s is given by the formula s 2 P=s. s
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Area of a Parallelogram The area A of a parallelogram with height h and base b is given by the formula A = bh. h b 9-3-12 Š 2008 Pearson Addison-Wesley. All rights reserved
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 1 A = h ( B + b) . 2 h B 9-3-13 Š 2008 Pearson Addison-Wesley. All rights reserved
Example: Area of a Parallelogram Find the area of the trapezoid below. 7 cm. 5 cm.
Solution
13 cm.
1 1 A = h ( B + b ) = (5) ( 7 + 13) 2 2 1 2 = (5) ( 20 ) = 50 cm. 2 Š 2008 Pearson Addison-Wesley. All rights reserved
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Area of a Triangle The area A of a triangle with base b and height h is given by the formula
1 A = hb. 2
h b 9-3-15
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Example: Area With Multiple Shapes Find the area of the shaded region below. 4 in.
Solution
4 in.
Area of square – Area of triangle
1 s − bh 2 1 2 2 4 − (4)(4) = 16 − 8 = 8 in. 2 2
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Circumference of a Circle The distance around a circle is called its circumference.
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Circumference of a Circle The circumference C of a circle of diameter d is given by the formula. C = π d, or equivalently r d C = 2π r , where r is a radius.
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Area of a Circle The area A of a circle with radius r is given by the formula.
A =πr . 2
r
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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 Circumference
C = 2π r = 2π (6) = 12π ≈ 37.68 in. Area 2 2 2 A = π r = π (6) = 36π ≈ 113.04 in. © 2008 Pearson Addison-Wesley. All rights reserved
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