Algebra 1 Word Problems - Area
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In the Area
Word Problems - Area

 
 There is a circular pond in front of the school.
 The pond is 20 feet in diameter.
 The school board wants to build a sidewalk around the pond.
 They want to make the sidewalk 3 feet wide.
 What is the area of the sidewalk?
 
 OK, so the pond has a diameter of 20 feet.
 A diameter is the distance 
 from one side of a circle to the other.
 
 A radius is the distance 
 from the center of the circle to the edge.
 The radius is one half of the diameter..
 
 So the radius of the pond is 10.
 

 
 The area of the circle is equal to pi (3.14159 ...)
 times the radius squared.
 

Area = pr2

 
 The area of the pond is ...
 

Area = (3.1416)(102)

Area = 314.2 square feet

 
 The sidewalk is to be 3 feet wide.
 The distance from the center of the circle
 to the outside of the sidewalk is 10 + 3 = 13 feet.

 

 If we didn't have a pond at all,
 but just a round slab of concrete with a radius of 13
 the area would be ...
 

Area = p(13)2

Area = p(169)

Area = 530.9 square feet

 
 But we DO have a pond in the middle.
 The area of the pond is 314.2 square feet.
 

 
 So the area of the 3 foot wide walk,
 is the area of the 13 foot radius concrete disk
 minus the area of the 10 foot radius pond 
 in the middle of it.
 
 Area of walk = 530.9 sq. ft. - 314.2 sq. ft.
 Area of walk = 216.7 sq ft.
 
 So this is the strategy you use with the 
 "border around the edge" problems.
 
 Find the area of the surface to the edge of the border
 Subtract the area of the thing in the middle.
 

   copyright 2005 Bruce Kirkpatrick

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