Module 2

Module 2: The Imperial System

 

Bringing Ideas Together

 

Square Foot

 

 

Square Yard

 

 

You have discovered that the squares having a side length of an inch, foot, or yard can be used as units of area. The related area units are square inch, square foot, and square yard.

 

As you discovered in Explore, 1 ft2 = 144 in2.

 

Why?

 

Also, you discovered 1 yd2 = 9 ft2.

 

Why?

 

Example 2

 

A wigwam, which is a semicircular structure originally made by First Nations people out of young tree saplings, has an interior close to the shape of a rectangle. The interior is 12 ft × 9 ft 3 in.

1. What is the area of the wigwam in square feet? Estimate your answer first, and then calculate the exact answer.
   
   
2. What is the area of the wigwam in square yards?

View the animated “Example 2 Solution.”

 

Example 3

 

Dawn bought wallpaper for her bedroom. The roll of wallpaper is in wide. Dawn’s walls are 8 ft high. She plans to cover the walls in vertical strips from floor to ceiling. What is the area that can be covered with one vertical strip of wallpaper?

 

Estimate first to predict an answer that would make sense.

 

Solution

 

Estimate first.

 

in is just less than 24 in, or 2 ft.

 

An 8-ft strip, which is 2 ft wide, covers 8 ft × 2 ft, or 16 ft2.

 

Now use your calculator to determine the area more precisely.

 

You must first convert in to feet.

 

 

 

 

Each strip of wallpaper covers ft2.

 

Try the following alternate solution using decimal values.

 

You must first convert in to feet.

 

 

Leave this answer on your calculator display.

 

 

Each strip of wallpaper covers about 13.67 ft2 (which is approximately ft2).

 

Self-Check

 

Respond to the questions that follow.

 

SC 1. Jasper wants to install a parquet floor in his kitchen. He sees an advertisement in a flyer that quotes prices per square foot. About how many square feet will Jasper need if the floor is a rectangle measuring 10 ft 9 in × 11 ft 6 in?

 

SC 2. A sheet of printer paper is 8.5 in × 11 in. Darcy says it is almost 1 ft2. Is Darcy correct? Explain your answer.

 

SC 3. Paula purchased a new home 1260 ft2 in area. What is the home’s area in square yards?

 

SC 4. Boris’s front lawn is rectangular and measures 50 ft × 30 ft. He purchased a fall fertilizer that must be applied at a rate of 6 lb per 1000 ft2. How many pounds of fertilizer should Boris apply?

 

SC 5. The sole of each of Norma’s moccasins is 36 in2 in area. When Norma stands with both feet flat on the floor, what is the total area in square feet that the moccasins cover?

 

SC 6. How many square inches are there in 1 yd2?

 

Compare your answers.

 

Beyond the Square Yard

 

Do you remember the units used in the SI (metric) system for describing larger areas, such as the area of a field or even the area of a province?

 

In the imperial system the acre and square mile are used to describe areas too large to be easily described by the square foot or square yard.

 

 

 

 

 

The acre was originally defined as the area of a field that could be ploughed by a single ox in one day. The word acre comes from the Old English word aecer, meaning field.

 

In the last half day of the nineteenth century, surveyors mapped Western Canada. The land was divided into squares that measured 6 mi on a side. These large squares were called townships.

 

 

A square mile was called a section, so there were 36 sections in a township. Each section was divided into quarters, or quarter sections. Each quarter section was one-half mile. These quarter sections were parcelled out as homesteads. Each quarter section was 160 ac in size. An acre, an imperial area measurement, is a square that measures approximately 70 yd on a side.

 

Today you can see evidence of this survey from the air. North-south roads in the country are 1 mi apart.

 

East-west roads are 2 mi apart. Seen from the air, the roads divide the countryside into rectangles measuring 1 mi by 2 mi in size. Each of these rectangles is two sections!

 

Example 4

 

An American football field is 360 ft × 160 ft. Is its area much smaller than, roughly the same as, or much larger than 1 ac?

 

Solution

 

Compare the area of the football field to an acre, 4840 yd2.

 

 

Convert this area to square yards. Recall, that 1 yd2 = 9 ft2.

 

 

An American football field is roughly 1 ac in area. In fact, it is 1.3 times larger than an acre, as you can see from this calculation.

 

 

You can use the interactive multimedia “Imperial System Area Conversion” to confirm the solution to the previous example.

 

You may also use this interactive to help you complete the Self-Check questions that follow.

 

Self-Check

 

Respond to the following questions.

 

SC 7. There are 160 ac in a quarter section. How many acres are there in a section that is 1 mi2 in area?

 

SC 8. When the Doukhobors immigrated to Canada from Russia in 1899, they were granted 773 400 ac for their farms and communities in what is now Saskatchewan and Manitoba. What is the area of this land grant in square miles?

 

SC 9. According to the United States Department of Agriculture, in 2009, American farmers planted 320.9 million acres to principal crops. What is this acreage in square miles?

 

SC 10. Using your answer from question 9, how long would the sides of a square be that enclosed 320.9 million acres? Express your answer to the nearest mile.

 

How do you find the side length of any square from its area? For example, what is the side length of a square having an area of 9 mi2?

 

Compare your answers.

 

It is often necessary to convert areas between the SI (metric) and imperial systems.

 

Example 5

 

Convert 1 in2 to square centimetres.

 

Solution

 

1 in = 2.54 cm

 

 

Remember that when you were working with linear measurements, you created tables to help convert between the SI (metric) and imperial measurement systems. As you will see in the next questions, you can do the same thing for area measurements.

 

Self-Check

 

Respond to the following questions.

 

SC 11. Complete a table like the following. Round to 4 decimal places when necessary. Two examples have been done for you.

 

Imperial	Metric
1 in2	6.4516 cm2
1 ft2	________ m2
1 yd2	________ m2
1 ac	0.4047 ha
1 mi2	________ km2

 

SC 12. Complete a table like the following. Round to 4 decimal places when necessary. Two have been done for you.

 

Metric	Imperial
1 cm2	________ in2
1 m2	________ ft2
1 m2	________ yd2
1 ha	2.4711 ac
1 km2	0.3861 mi2

 

Compare your answers.

 

The tables you completed in SC 11 to SC 12 may help you simplify conversions between systems.

 

Example 6

 

The area of Jasper’s living room is 180 ft2. What is the area in square metres?

 

Solution

 

 

So,

 

 

The living room area is about 16.722 m2.

 

Self-Check

 

Do the following questions. Use the information from the tables in SC 11 to SC 12.

 

SC 13. Nick planted 320 ac of canola. How many hectares of canola did he plant? Round your answer to 1 decimal place.

 

SC 14. The area of Morris’s front lawn is 100 yd2. What is the area in square metres? Round your answer to the nearest unit.

 

SC 15. The printed area of a wedding invitation is 150 cm2. What is the area in square inches? Round your answer to 1 decimal place.

 

Compare your answers.

 

You may wish to do SC 13 to SC 15 a second time using a conversion tool found on the Internet.

 

Mastering Concepts

 

Try this question.

 

In 2009, in Canada, about 141 000 new homes were constructed. If the average size of each home were 1800 ft2 in area, how many square miles of new homes does this represent? Express your answer to the nearest square mile.

 

Compare your answer.

 

Mathematics 10-3 Learn EveryWare © 2010 Alberta Education