Two similar figures have a linear scale factor of 4. What is the ratio of their area's?
The ratios of the areas of similar figures are proportional to the square of their corresponding sides.
so small area : larger area = 1^2 : 4^2 = 1 : 16
To find the ratio of their areas, we need to know that the area of a figure is proportional to the square of its linear dimensions.
Since the linear scale factor between the two figures is 4, it means that every linear dimension (length, width, height, etc.) of the second figure is 4 times larger than the corresponding dimension of the first figure.
Therefore, the ratio of the areas of the two similar figures is equal to the square of the linear scale factor.
In this case, the ratio of their areas is 4^2 = 16. So, the second figure has an area that is 16 times larger than the first figure.
To find the ratio of the areas of two similar figures, we'll use the scale factor. Given that the linear scale factor between the two figures is 4, we know that every length in the second figure is four times greater than the corresponding length in the first figure.
The area of a two-dimensional figure is determined by multiplying the length of one side by the length of another side. If the scale factor is 4 for both sides, the ratio of their areas will be the square of the scale factor.
In this case, the scale factor is 4, so the ratio of the areas can be calculated as follows:
Ratio of areas = (scale factor)^2 = 4^2 = 16
Therefore, the ratio of the areas of the two similar figures is 16:1.