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Area Conversion between
Imperial and Metric
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Skills Application: Area Conversion between Imperial & Metric
Step-by-Step: Area Conversion between Imperial & Metric
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## Tagged in

In ancient times measurements were made using the body, however this was problematic because of the difference in body size among people. At first an inch was the width of a man's thumb. Then King Edward ruled that 1 inch equalled 3 grains of barley placed end to end lengthwise. The foot was the length of the average man's foot about 11 ¼ inches. A yard was originally the length of a man's girth, then in 1266 King Henry set the length of yard to be the distance from his nose to the thumb of his out-stretched arm. Today, units of measure are standardized by measuring the distance light travels in a fraction of time.

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The units inch, foot, yard and mile are called imperial units of measure of length and the square of them are called imperial units of measure of area.

#### Conversion between Imperial Units of Measure of Area

We know that 1 foot equals 12 inches. So, the area of a square with 1-foot-long sides will be equal to the area of square with 12-inch-long sides. Consider the following figure:

Therefore, 1 ft2 = 144 in2
Likewise, 3 feet equals 1 yard. So, 9 ft2 = 1 yd2 .

Also, 5280 feet = 1 mile. Consequently, 27,878,400 ft2 = 1 mi2.

#### Metric Units of Measure of Area

There is another system for measurement which is called metric system. The units of measuring length in the metric system are millimeter, centimeter, meter and kilometer. One can change one unit in the metric system to the others very easily. In the following table you could find the relation between metric units of measure length and area.

##### CONVERSION

Metric Area Units
1 square centimeter (cm2 ) = 100 square millimeters (mm2 )

1 square decimeter (dm2 ) = 100 square centimeter (cm2 )
1 square meter (m2 ) = 100 square decimeter (dm2 )

To convert from square meters to square decimeter, square decimeters to square centimeters, and square centimeters to square millimeters, we use multiplication.

Example:

2 square meters = 2 x 100 = 200 square decimeters since 1 square meter = 100 square decimeter.

To convert from square decimeter to square meters, square centimeters to square decimeters, and square millimeters to square centimeters, we use division.

Example:

400 square centimeter = 400 ÷ 100 = 4 square decimeters because 100 square centimeter = 1 square decimeter.

### A Short Review

You need to know 2 things:
• the conversion factor, and
• the magnitude of units to be converted. (i.e. which is bigger)

For example the m2 is bigger than dm2 and not the other way around.

If converting a bigger unit to a smaller, multiply by the conversion factor.

5 ft2= 5 x 144 = 720 in2

5 m2= 5 x 100 = 500 dm2

If converting from a smaller to a bigger, divide by the conversion factor.

5 in2= 5 ÷ 144 = 0.034 in2

5 dm2= 5 ÷ 100 = 0.05 m2

### Worksheet: Level 1

The operations used are clearly specified. Only one type of mathematical operation is used in a task.

### Worksheet: Level 1 Sample Questions

Multiply to get the area conversion factors:

Area conversion factors are calculated by squaring the conversion number between any 2 units. Square each linear conversion number to calculate the area conversion factors.

Example:

Since 3 feet make a yard, what is the conversion factor between ft² and yd²?

3 × 3 = 9

Question:

1. If 12 inches make a foot, what is the conversion factor between ft²and in²?

Further Examples:

What is the conversion factor between:

1. feet and inches?
2. square feet and square inches?
3. cm and m?
4. cm² and m²?

### Worksheet: Level 1 Answer Key

1. 12 × 12 = 144

### Worksheet: Level 2

Tasks involve one or two types of mathematical operation. Few steps of calculation are required.

### Worksheet: Level 2 Sample Questions

Convert the following.

Remember: The conversion factor between inand ftis 144, between ftand ydis 9. Metric conversion factors between cm2 and m2 is 10,000 , between mm2 and cm2 is 100.

When converting from a bigger unit of measure to a smaller one, the bigger unit gets
MULTIPLIED by their conversion factor.

Example:
5 ft2 = ____ in² (feet are bigger than inches) 5 ft2 = 5 × 144 = 720 in²

When converting from a smaller unit of measure to a bigger one, the smaller unit gets
DIVIDED by their conversion factor.

Example:
100 in² = ____ ft² (inches are smaller than feet) 100 in² = 100 ÷ 144 = 0.6944 ft²

Question:

1. 3 ft2 = _____ in²

Further Examples:

Convert the following:

5.25 m² = _____ cm²

31,000 in² = _____ ft²

### Worksheet: Level 2 Sample Answer Key

1. 3 ft² = 3 × 144 = 432 in²

### Worksheet: Level 3

Tasks require a combination of operations. Several steps of calculation are required.

### Worksheet: Level 3 Sample Questions

Convert the following:

Remember, when converting from a bigger unit of measure to a smaller one, the bigger unit gets MULTIPLIED by their conversion factor.

Example:
5 ft² = _____ in² (feet are bigger than inches) 5 ft2 = 5 × 12² = 720 in²
When converting from a smaller unit of measure to a bigger one, the smaller unit gets
DIVIDED by their conversion factor.

Example:
100 in² = _____ ft² (inches are smaller than feet) 100 in² = 100 ÷ 12² = 0.6944 ft²

Sometimes there are 2, 3, or more jumps between theunitsto be converted. In this case, you have to use 2, 3 or more conversion factors for multiplying or dividing by.

Examples:
4.5 mi² = _____ ft² (there are3 ft in a yd AND 1760 yd in a mi)
4.5 mi² = 4.5 × 3²  × 1760² = 125, 452, 800 ft²

3060 cm² = _____ km² (there are 100 cm in a m AND 1000 m in a km)
3060 cm² = _____ 3060 ÷ 100²  ÷ 1000² = 0.000000306 km²

Question:

1. 3 m² = _____ mm²

Further Examples:

Convert the following:

3.14 mm² = _____ km²

84,275,822 in² = _____ mi²

### Worksheet: Level 3 Sample Answer Key

1. 3m² = 3 × 1000² = 3,000,000mm²

Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required.

### Measurement math connections for trades & technology

Length or Distance is a 1-D or 1 dimensional concept. It means it runs in 1 direction or in a single line. For this reason it is called linear. It can be measured directly with rulers, tape measures, reflected laser beams in distance finders.

There are many synonyms or alternative names for Length. Some of these names include radius, caliber, depth, or edge. (See table below) These are all linear concepts. Any 2 of these can combine to indicate Area. For example Depth and Length of a trench can combine to express the Sidewall Area of a trench to be shored against collapsing, or Width and Thickness can combine to express the Cross-Sectional Area of metal in a spoons handle.

Area is a 2-D or 2 dimensional concept. It can relate to shapes (2-D things) and objects (3-D things). It spreads in 2 linear directions or in a surface plain. For this reason it is called planar. It can not directly be measured since measurement tools are linear. Planar (area) “measurements” are always calculated from linear measurements. Some digital instruments say they “measure” Area, but it cannot be measured directly. These instruments calculate area from reflected laser beam Distance measurements.

Area surfaces can be very irregular or very smooth and regular. Area coverage can be partial or full.

Area can be measured in Metric or Imperial units, many of these are used only in specific industries. For example land area in acres is mostly applicable to real estate lot sizes. Forest and lake sizes are measured in square kms. The effective surface area in square feet of an air filter cloth or paper inside an air filter is only used in automotive parts context or in ductwork with an air exchange unit. Queen size sheets cover the area of a queen size bed – a concern for the manufacturing industry.

Many units of measure of Area originate from linear units of measure but are modified to reflect that they are used for expressing size of Area. In this process linear units of measure become planar. Examples include in → in2, km → km2, yd → yd2.

Sometimes these units can be spelled this way: sq.ft. or square feet, sq. kms or square kilometers. Regardless of spelling variations they are still planar units of measure for Area.

Some other units of measure words show no relation to linear units, but they are. Examples include acre (= strip of land the length of 1 furlong & the width of 1 chain, well spare you the history lesson here on what chain that is, etc.), hectar (simply = 10,000m2 size of land), a roofing square (not a layout tool, simply = 100 sq.ft. unit). Some area units of measure are funny or anecdotal, they work unofficially as figures of speech. “A truck the size of a dinosaur” relates to area (especially the front), so does “ 5 holes totalling the size of my hand”. It could be meaningfully used to indicate Area during rescue or evacuation.

### Additional Information: Sample Definitions & Conversion Data Table

 Property of matter being measured: possible synonyms symbol Unit of measure Metric symbol Imperial & US symbol Distance (1-D) in straight line: straight lines of circles: loops (full or part) & : length, width, height, depth, thickness, gauge, side, edge, strain L or l, w, h, d           th, ga. s, e, ε (greek epsilon) meter and other prefixes (kilo, centi, …) m mile, fathom mi, fm diameter, caliber, bore, radius, chord d or Ø, cal, b or Ø,  r, ch furlong, yard fur, yd perimeter, circumference, arc, stroke p or P     C                 a, s feet, inch             barleycorn, point ft, in              - , pt Area (2-D) surface area, coverage, wrap A meter squared and other prefixes (kilo, centi, …) hectar m² ha square mile, square yard, square feet, square inch mi², yd²      ft², in² acre ac circular mils               square mils CMs        SMs