Sunday, 17 August 2008

Perimeter and Circumference

In geometry, we often come across 2 terms "Perimeter" and "Circumference".

What is the difference between them?

Let us discuss about Perimeter first before comparing the geometrical terms.

The term "Perimeter" refers to the length of the outline of a shape (with clear start and end points).

It is applicable to shapes using straight lines as their borders.

From the rectangle shown above, we can conclude that its periemeter is

(Q + P + Q + P) = 2Q + 2P units long.

- Perimeter is NOT the same as area, which is the region within the defined boundary.
- Perimeter is the length of the boundary.

Now, what is "Circumference"?

Circumference is the length of the outline of circle.

It is not as simple as adding up all the borders defining its region. This is so since there is no straight line governing its boundaries. It is all curves!

Therefore a formula has been derived to calculate this special geometrical term.

Circumference = 2 (pi) r

An observation is that the larger the radius "r", the larger is the circumference.

Again, note that circumference is different from area.



Irregular Shapes

Sometimes, we encounter shapes that are a combination of rectangles, squares, rhombus, and circles, etc, or part of them. See below.

In this instance, what you need to do to compute the length of the boundary is to break up the odd irregular shape into its individual components as shown on the right figure of the diagram above.

Here the original shape is revealed to have 2 different shapes (Rectangle and Circle). Computation of the length of the border will then be simplified and more straight forward.

In conclusion, as long as the principles of calculating the perimeter and circumference are understood, computation of the length of any shape will be a breeze. :)


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