## Area and Volume scale factor

## Summary

Two figures/shapes may be identical in shape but generally not in size. The following shapes will always be similar in shape but not in size.

## Linear scale factor

A shape can be transformed into another similar shape by adjusting its size through enlargement/reduction by using a scale factor. In this process all dimensions of the shape must stay proportional to each other (i.e the lengths, heights, or widths)

For example a scale factor of 2 means that the new shape is twice the size of the original shape. A scale factor of 3 means that the new shape is three times the size of the original.

To carry out enlargements/reductions you must first find the scale factor. To find the enlargement scale factor you divide the dimensions of the big shape by the small shape.

To find the shape reduction scale factor you divide the small dimensions by the big dimensions.

Below is an example.

## Area Scale Factor

Area scale factor can apply to any shape provided you have at least one of the corresponding quantities (areas or lengths) For example here are two triangles; There are simple steps you will take to find the area of the large triangle;^{2}

## Volume Scale Factor

The same strategy applies to volume scale factors, except you have to be aware that volumes are cubic roots. For example your might have the following two bottles whose lengths are known and just one volume, and you have to find the other volume.## Summary

Two figures/shapes may be identical in shape but generally not in size. The following shapes will always be similar in shape but not in size.

## Linear scale factor

A shape can be transformed into another similar shape by adjusting its size through enlargement/reduction by using a scale factor. In this process all dimensions of the shape must stay proportional to each other (i.e the lengths, heights, or widths)

For example a scale factor of 2 means that the new shape is twice the size of the original shape. A scale factor of 3 means that the new shape is three times the size of the original.

To carry out enlargements/reductions you must first find the scale factor. To find the enlargement scale factor you divide the dimensions of the big shape by the small shape.

To find the shape reduction scale factor you divide the small dimensions by the big dimensions.

Below is an example.

## Area Scale Factor

Area scale factor can apply to any shape provided you have at least one of the corresponding quantities (areas or lengths) For example here are two triangles; There are simple steps you will take to find the area of the large triangle;^{2}