Calculating the scale factor for making shapes bigger or smaller is pretty easy and can be really fun once you know how to do it!

The scale factor shows you how much a shape gets bigger or smaller when you change its size. Here’s how you can figure it out:

Step 1: Know the Original and New Sizes

First, you need to find out the sizes of the original shape and the new shape after you change it.

For example, let’s say you have a triangle. Its base is 4 cm and its height is 3 cm.

If you make this triangle bigger so that the base is now 8 cm and the height is 6 cm, those numbers are what you’ll use.

Step 2: Use the Simple Formula

The formula to find the scale factor is easy:

Scale Factor = New Size ÷ Original Size

Using our triangle example, let's find the scale factor for the base:

Scale Factor for Base = 8 cm ÷ 4 cm = 2

Now let's find the scale factor for the height:

Scale Factor for Height = 6 cm ÷ 3 cm = 2

Step 3: Make Sure It’s the Same

When you calculate the scale factor for all the sizes, they should match.

This means if one part says the scale factor is 2, then all the parts should also say 2. If they don't, you might have made a mistake!

Step 4: Understand What the Scale Factor Means

If the scale factor is more than 1, it means the shape has gotten bigger.

For example, a scale factor of 2 means the shape is now twice as big as before.

If the scale factor is less than 1 (like 0.5), it means the shape has been shrunk to half its original size.

Quick Recap

• Original Triangle: Base = 4 cm, Height = 3 cm
• Bigger Triangle: Base = 8 cm, Height = 6 cm
• Scale Factor: 2 (for both base and height)

And that’s it! Figuring out the scale factor is not just useful for math, but it can also be really cool when you're resizing things in art or design!