Scale factors make each of the sides of a shape (two dimensional figure) or solid (three dimensional figure) bigger by a certain amount. Sometimes it is important for us to know how this affects the perimeter of a shape.

Let's look at these ideas separately.

How does scale factor affect perimeter?

How does scale factor affect area?

Summary




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How does the scale factor affect perimeter?


Perimeter is the sum of all the sides of a shape (to get perimeter add all the sides), so let's look at some examples of how scale factor affects addition:

For example:


The perimeter is 16


Suppose the scale factor is 2, this means that we multiply each side by 2 the sum is:



The new perimeter is 32

When we doubled the sides the perimeter was doubled.

Another example of perimeter:



The perimeter is 120


Suppose the scale factor is one half, this means that we multiply each side by one half (or divide each side by 2) the sum is:



The new perimeter is 60

When we halfed the sides the perimeter was halfed.















How does the scale factor affect area?

The way that scale factor affects area is different from perimeter. The reason why is that area involves multiplication but on the most basic level perimeter involves addition. Let's look at a few examples:




For example:



The area is 15

Suppose the scale factor is 2



The area is 60

When we used a scale factor of two did that double the area or did it cause the area to be multiplied by 4 (quadrupled)?

Since


We can see that the area was multipled by 4 (quadrupled)


Another example:



The area is 96

Suppose the scale factor is one half



The area is 24

When we used a scale factor of one half did that half the area or did it cause the area to be multiplied by one fourth (quartered)?

Since


We can see that the area was multipled by one fourth (quartered)?



The units for area and perimeter give us a hint about what happens here.
Perimeter units do not change (if the sides are in feet then the perimeter is also measured in feet)

Area units do change( if the sides are in feet then the area is measured in square feet; square feet is the same as feet times feet)

Since the scale factor is applied to each side you have to multiply scale factor times scale factor to see what happens.


The following video explains the concept a little more (linear measurements involve perimeter; also remember that scale factors can also be represented as ratios like we have in the video):









Summary





Remember

Perimeter is changed by the scale factor

Area is changed by (scale factor times scale factor)

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Missouri City Middle School Eighth Grade Math Class

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