In scale drawings, the size of items changes based on something called the scale factor.

1. Scale Factor: If we say the scale factor is $k$, it means we multiply all the lengths by $k$.

2. Area Calculation: The area, which is how much space something takes up, changes by the square of the scale factor. So, if we change the lengths by a factor of $k$, the area changes by a factor of $k^2$.

Let’s look at a couple of examples:

• If we double a length (which means $k=2$), the area becomes 4 times bigger. This is because $2^2 = 4$.

• If we cut a length in half (which means $k=0.5$), the area gets smaller by a factor of 0.25. That’s because $(0.5)^2 = 0.25$.

Understanding how these numbers work together is really important for reading scale drawings correctly.