Introduction to Area and Perimeter

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INTRODUCTION TO AREA and PERIMETER

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Here is a good resource for area and perimeter information:   http://www.mathleague.com/help/geometry/area.htm

Take a piece of paper and a pencil.
Put your pencil on the paper and draw anything you want, with the following conditions:
you must return to your starting point, and you are not allowed to cross over anything you have drawn on the way there!
The resulting curve is called a simple closed plane curve.
It is a curve that lies in a plane; it is closed because it starts and ends at the same place; and it is simple because it never crosses itself.

Every figure that is created in this way has an inside (the region enclosed by the curve) and an outside (the region not enclosed by the curve).

When you are asked for the "area" of a simple closed plane curve, this means the area inside the curve.
For example, the area of a rectangle is the area inside the rectangle, and the area of a triangle is the area inside the triangle.

DEFINITION: The area of a simple closed plane curve is the size of the region enclosed by the curve.

Whereas area measures the space "inside" a figure, we can also ask about the distance "around" a figure:

DEFINITION: The perimeter of a simple closed plane curve is the length of the simple closed curve that defines it.

Quite a mouthful! Probably more than you want to hear right now! The definition looks simpler if we specialize it to polygons:

DEFINITION: The perimeter of a polygon is the sum of the lengths of all its sides.

Note that your teacher might ask you to "trace a perimeter" or "shade an area".

Perimeter is measured using units of length.
These are all valid units for perimeter:   centimeter (cm), meter (m), kilometer (km), inch (in), foot (ft), yard (yd), mile (mi)

Area, on the other hand, is measured using "square units":
A square that has sides of length one inch is called a square inch; it has an area of 1 in².
A square that has sides of length one centimeter is called a square centimeter; it has an area of 1 cm².
A square that has sides of length one mile is called a square mile; it has an area of 1 mi².
If blah is any unit of length, then a square that has sides of length blah is called a square blah; it has an area of 1 blah².

These are all valid units for area:   cm², m², km², in², ft², yd², mi²

Here are some basic formulas:

AREA OF A RECTANGLE:
A rectangle with length l and width w has area A given by A=lw .

AREA OF A SQUARE:
A square with sides of length l has area A given by A= l 2 .

PERIMETER OF A RECTANGLE:
A rectangle with length l and width w has perimeter P given by P=2l+2w .

PERIMETER OF A SQUARE:
A square with sides of length l has perimeter P given by P=4l .

On this exercise, you will not key in your answers.
However, you can check to see if your answer is correct.

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