Final answer:
To determine the scale factor required to enlarge a trapezoid to a specified area, the square root of the ratio of the new area to the original area is calculated. For instance, to get from 100 square units to 900 square units, we need a scale factor of 3, as the square root of 9 (the ratio of the areas) is 3.
Step-by-step explanation:
The question inquires about the scale factor needed to enlarge a trapezoid from an area of 100 square units to various larger areas. To determine the necessary scale factor, we use the rule stating that the ratio of areas of similar figures is the square of the scale factor. For instance, if the original area is 100 square units and we want to increase it to 6400 square units, we need to find a factor that when squared gives us 64 (since 6400 is 64 times 100). The scaling process involves squaring the scale factor to scale the area, not just multiplying by the scale factor directly.
To scale a figure to have an area of 6400 square units from 100 square units, we calculate the square root of 64, which is 8. Thus, the required scale factor is 8. Following similar processes with different target areas, the scale factors would be:
- For 900 square units: Square root of 9 (since 900 is 9 times 100), which gives us a scale factor of 3.
- For 100 square units: Square root of 1 (since 100 is 1 times 100), which gives us a scale factor of 1.
- For 25 square units: Square root of 0.25 (since 25 is 0.25 times 100), which gives us a scale factor of 0.5.
- For 4 square units: Square root of 0.04 (since 4 is 0.04 times 100), which gives us a scale factor of 0.2.
According to the options provided, a scale factor that corresponds to one of the given areas is not listed. However, the closest one, being option b (900 square units), would require a scale factor of 3 because the square root of 9 is 3 (9 being the factor by which 100 square units is multiplied to get 900 square units).