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.

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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.

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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

P = 2l + 2w,

or equivalently

P = 2(l + w).

w

l

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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

P = 4s.s

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

A = lw.

w

l

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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

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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

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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.

b

h

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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

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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

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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

h

b

1 .2

A hb

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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

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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.

or equivalently

where r is a radius.

,C d

2 ,C r d r

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Area of a Circle

The area A of a circle with radius r is given by the formula.

2.A rr

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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

2 2 (6) 12 37.68 in.C r Circumference

Area2 2 2(6) 36 113.04 in.A r