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Definition of Area
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Skills Application: Definition of Area
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In the ancient Roman Empire the Latin word “area” meant an empty lot, a vacant piece of land. Today the meaning of area did not change much and it became a widely used math word. The term area in math context today relates to the size of any kind of surface.

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Area is a measure of how much space there is on a flat surface,

For example: the size of an apartment is 150 square feet, or a piece of land is 1250 square meters, or the area of Canada is 9,984,670 square kilometers. In all of these examples we talk about area.

For example two sheets of paper have twice the area of a single sheet, because there is twice as much space to write on.

On the other hand area is measured by the number of square units that cover a closed figure. Area is measured in square units.

The area of this square is 16 square units.

That means 16 square units are needed to cover the surface within the square. We can use different square units. For example, a square meter is a square with all sides that are one meter in length. In the same way, a square foot is a square with all sides that are one foot in length.

NOTATION

There is a shorthand way of writing a square unit. We write the letter(s) for the unit with a superscript 2 after it, like this:

8 square meters is written as 8 m²

8 square feet is written as 8 ft²

### A Short Review

Area or surface area means surface coverage. Shapes and objects have surfaces. In everyday context the idea of area might be expressed using different words, such as lot size, roof size, bed size, shirt size, wire size.

This coverage is usually measured in square shapes such as square feet, square meters, square inches.

A square foot is a square with a length of 1 foot and a width of 1 foot. A square cm is a square with a length of 1 cm and a width of 1 cm.

Some other units of measure dont seem related to area first, but they are: acre, king size, XXL, circular mils are all units of area.

### Worksheet: Level 1

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

### Worksheet: Level 1 Sample Question

Examples:

How many surfaces does a tissue box have?
How many surfaces does an entry door have?
How many surfaces on a mirror get cleaned?
How many surfaces on a window get cleaned?
On a cube shaped molar tooth how many surfaces can be cleaned? Why not all?
Is it true that pressure measured in psi (pounds per square inch) is derived from area? Why or why not?

Further examples:

Which of the following 5 units of measure are used when measuring Area?

a) m     b) m2     c) hectare     d) m³     e) ft³     f) in     g) ft²     h) mi²     i) acre

### Worksheet: Level 1 Answer Key

a) m       b) m2     c) hectare     d) m³      e) ft³     f) in     g) ft²     h) mi²     i) acre

### Worksheet: Level 2

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

### Worksheet: Level 2 Sample Question

Example:

Which math concept is expressed in the following examples:

Length? Area? or Perimeter?

-          belt size
-          plate size
-          single bed size
-          an asteroid the size of Texas
-          inseam
-          bathroom size
-          a parcel the size of a football field
-          tile size
-          hat size
-          couldnt hit a barn door from 10 feet

Further examples:

Understanding concepts of terminology

True or False?

(a) A boat does not have area.

### Worksheet: Level 2 Sample Answer

(a) False, all shapes and objects have area.

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

Measurement math connections for trades & technology

Area is a 2-D or 2 dimensional concept. It always implies Length and Width that cover a 2-D shape or a 3-D object. Surfaces can be very irregular or very smooth and regular. 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 measured in square kms is related to surveying and mapping. The effective surface area in squre 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 must cover the area of a queen size bed – a concern for the manufacturing industry.

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 first aid, rescue or evacuation.