Scale factors are a great way to look at different shapes and see how they are related.
When we talk about scale factors, we mean the ratio of matching lengths in two similar shapes.
For example, imagine a triangle with sides that are 4 cm, 5 cm, and 6 cm long. If there’s another triangle that looks just like it but has sides that are 8 cm, 10 cm, and 12 cm long, the scale factor is 2. This means the second triangle is twice as big as the first one.
How to Use Scale Factors to Compare Shapes:
Changing Sizes: If you know the scale factor, it’s easy to find the lengths of sides or the areas of a new shape. For instance, if a square has a side of 3 cm and we scale it by a factor of 4, the new square's side will be 3 cm times 4, which equals 12 cm.
Comparing Areas: The area changes with the square of the scale factor. So, if the scale factor is 2, the area increases by a factor of 2 times 2, which equals 4. If the original area is 9 cm², the new area will be 9 cm² times 4, giving us 36 cm².
Understanding scale factors helps us see how sizes and areas change. This makes it easier to compare and analyze different geometric shapes.
Scale factors are a great way to look at different shapes and see how they are related.
When we talk about scale factors, we mean the ratio of matching lengths in two similar shapes.
For example, imagine a triangle with sides that are 4 cm, 5 cm, and 6 cm long. If there’s another triangle that looks just like it but has sides that are 8 cm, 10 cm, and 12 cm long, the scale factor is 2. This means the second triangle is twice as big as the first one.
How to Use Scale Factors to Compare Shapes:
Changing Sizes: If you know the scale factor, it’s easy to find the lengths of sides or the areas of a new shape. For instance, if a square has a side of 3 cm and we scale it by a factor of 4, the new square's side will be 3 cm times 4, which equals 12 cm.
Comparing Areas: The area changes with the square of the scale factor. So, if the scale factor is 2, the area increases by a factor of 2 times 2, which equals 4. If the original area is 9 cm², the new area will be 9 cm² times 4, giving us 36 cm².
Understanding scale factors helps us see how sizes and areas change. This makes it easier to compare and analyze different geometric shapes.