A rectangle has an area of 20cm^2. Its length and width are each enlarged by scale factor 3. What is the area of the enlarged rectangle?

For questions regarding enlargements of shapes, it's sometimes easier to consider one dimension at a time. So for this example, let's first consider what the area of the rectangle would be if we just enlarged the length by a scale factor of 3. We can do this by multiplying the area by 3:

20cm^2 * 3 = 60cm^2

Now, let's consider enlarging the width of this rectangle by a scale factor of 3:

60cm^2 * 3 = 180cm^2

Notice that we end up multiplying the area of the rectangle by 3^2. The 3 is the scale factor that we're asked to enlarge by, and the 2 is the number of dimensions that we are enlarging the shape in.