UNIT 2 MODULE 6

PROBLEMS INVOLVING AREA

 

EXAMPLE 2.6.1

The diagram below shows the rectangular pen in which Gomer confines his wolverines and badgers. As a special treat, Gomer is going to cover the badgers' area of the pen with Astroturf. Assuming that Astroturf costs $1.25 per square foot, how much with this project cost? (Choose the closest answer.)

A. $1500
B. $9000
C. $4500
D. $3000

see solution

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EXAMPLE 2.6.2

The diagram below shows the plan for a new parking lot at the Southwestdale Mall. It is estimated that such construction costs $12 per square yard. What will be the total cost for the parking lot?

A. $2,073,600
B. $691,200
C. $6,220,800
D. $518,400

see solution

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EXAMPLE 2.6.3

The area enclosed by the racetrack below will be landscaped. Find the total cost if landscaping costs $2.00 per square yard. Chose the closest answer.



A. $41,258
B. $60,944
C. $20,315
D. $123,774

see solution

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EXAMPLE 2.6.4

The diagram below shows a circular pizza whose diameter is 8 inches, situated in a square box whose side length is 10 inches. How much of the box is "empty?"



see solution

 


EXAMPLE 2.6.5

The diagram below shows one exterior wall of a house. The wall has a door opening that measures 3 feet by 7 feet, and two window openings that each measure 6 feet by 4 feet. The wall, but not the openings, will be covered with siding material that costs $1.50 per square foot. Find the total cost of the siding material.

A. $400.50
B. $292.50
C. $499.50
D. $333.00

see solution

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EXAMPLE 2.6.6

Which is larger: a square cake pan that measures 8 inches on each side, or a circular cake pan with a diameter of 9 inches?

see solution

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EXAMPLE 2.6.7

A real-life encounter with GEOMETRY.

 

An acre is about 40,000 square feet, so you can imagine an acre to be a square area measuring 200 feet on each side. Several years ago, I was interested in hiring a bulldozer operator to clear a square parcel of land that measured 100 feet on each side. During a telephone discussion, one contractor offered the following: "I charge $600 per acre. An acre measures 200 by 200 feet, so a 100 by 100 foot plot would cost $300."

 

Why did I hang up?

 

 

 

 

 

 

 

 

 

 

 

 

EXAMPLE 2.6.8

Suppose that it costs $480 to build a rectangular wooden deck that measures 6 feet by 8 feet. Assuming that the cost of such an object depends upon its size (area), how much would it cost to build a similar deck measuring 18 feet by 24 feet?

A. $640
B. $1440
C. $1,920
D. $4,320

see solution

 

 

EXAMPLE 2.6.9

A circular pizza that is 16 inches in diameter costs $12.00. Assuming that the cost of such a pizza depends upon its size (area), what would be the cost of a pizza that is 8 inches in diameter?

 

A. $3.00
B. $4.00
C. $6.00
D. $8.00

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see solution

read a pizza-related haiku by Gomer





EXAMPLE 2.6.10

The morning after a party, Gomer finds on his living room carpet a circular purple wine stain with a diameter of 1 foot. Homer's Carpet Service charges him $30 to remove the stain. Assuming that the cost of removing such a stain depends upon its size, how much would it cost to remove a stain that 18 inches in diameter?

A. $45.00
B. $67.50
C. $54.00
D. $90.00

see solution

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EXAMPLE 2.6.11

Suppose that it takes 12 hours to decontaminate a circular chemical spill that has a radius of 6 feet. Assuming that the amount of time required to decontaminate such a spill depends upon its size (area), how many hours would it take to decontaminate a similar spill with a radius of 3 feet?

A. 4.5 hours
B. 6 hours
C. 1.5 hours
D. 3 hours

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see solution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EXAMPLE 2.6.12

Gomer's bathroom wall measures 8 feet high and 8 feet wide. He is going to cover the wall with square tiles that measure 2 inches by 2 inches. How many tiles are required to cover the wall?

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EXAMPLE 2.6.13

The diagram below shows a city park that will be landscaped, at a cost of $2 per square yard. Find the total cost of this project.



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see solution

 

 

 

 

 

 

 

 

 

 

 

 

 

EXAMPLE 2.6.14

The diagram below shows the courtyard at the Institute for Wolverine Studies. The shaded area represents lawn, while the circular area is a pool. Gomer has a contract to mow the lawn. He charges $0.02 per square foot for this service. Find the total cost for this job (he will mow the lawn, but not the pool).

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see solution

 





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