copyright 2013, 2010, 2007, pearson, education, inc. section 9.3 perimeter and area

Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 9.3

Perimeter and Area


What You Will Learn

PerimeterArea

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Definitions

The perimeter, P, of a two-dimensional figure is the sum of the lengths of the sides of the figure.

The area, A, is the region within the boundaries of the figure.

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Formulas

P = s1 + s2 + b1 + b2

P = s1 + s2 + s3

P = 2b + 2w

P = 4s

P = 2l + 2w

Perimeter

Trapezoid

Triangle

A = bhParallelogram

A = s2Square

A = lwRectangle

Area Figure

12A bh

11 22 ( )A h b b

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Formulas

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Example 1: Sodding a Lacrosse FieldRob Marshall wishes to replace the grass (sod) on a lacrosse field. One pallet of Bethel Farms sod costs $175 and covers 450 square feet. If the area to be covered is a rectangle with a length of 330 feet and a width of 270 feet, determinea) The area to be covered with sod.

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Example 1: Sodding a Lacrosse Fielda) the area to be covered with sod.

Solution

A = l • w = 330 • 270 = 89,100 ft2

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Example 1: Sodding a Lacrosse Fieldb) Determine how many pallets of sod

Rob needs to purchase.

Solution

Rob needs 198 pallets of sod.

Area to be covered

Area covered by one pallet

89,100

450 198

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Example 1: Sodding a Lacrosse Fieldc) Determine the cost of the sod

purchased.

Solution

The cost of 198 pallets of sod is198 × $175, or $34,650.

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Pythagorean TheoremThe sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse.

leg2 + leg2 = hypotenuse2

Symbolically, if a and b represent the lengths of the legs and c represents the length of the hypotenuse (the side opposite the right angle), then

a2 + b2 = c2 a

b

c

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Example 2: Crossing a MoatThe moat surrounding a castle is 18 ft wide and the wall by the moat of the castle is 24 ft high (see Figure). If an invading army wishesto use a ladder to cross the moat andreach the top of thewall, how long mustthe ladder be?

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Example 2: Crossing a MoatSolution

c2 a2 b2

c2 (18)2 (24)2

c2 324 576

c2 900

c2 900

c 30The ladder needs to be at least 30 ft long.9.3-12


CirclesA circle is a set of points equidistant from a fixed point called the center.A radius, r, of a circle is a line segment from the center of the circle to any point on the circle.A diameter, d, of a circle is a line segment through the center of the circle with both end points on the circle.

d

r

circumference

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Circles

The circumference is the length of the simple closed curve that forms the circle.

d

r

circumference

C 2 r

A r2

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Example 4: Determining the Shaded AreaDetermine the shaded area. Use the π key on your calculator and round your answer to the nearest hundredth.

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Example 4: Determining the Shaded AreaSolutionHeight of parallelogram is diameter of circle: 4 ft

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Example 4: Determining the Shaded AreaSolution

Area of parallelogram = bh= 10 • 4 = 40 ft2

Area of circle = πr2 = π(2)2

= 4π ≈ 12.57 ft2

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Example 4: Determining the Shaded AreaSolution

Area of shaded region =Area of parallelogram – Area of circleArea of shaded region ≈ 40 – 12.57Area of shaded region ≈ 27.43 ft2

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Homework

P. 507# 5 – 32 all, 33 – 54 (x3)

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copyright 2013, 2010, 2007, pearson, education, inc. section 9.3 perimeter and area

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