Final answer:
To determine the area of the larger polygon, square the ratio of sides (3:2), giving 9/4, and multiply this by the smaller area, 24 cm², resulting in an area of 54 cm² for the larger polygon.
Step-by-step explanation:
The question involves finding the area of a larger polygon based on its similarity and scale factor relative to a smaller polygon. Given that the ratio of the sides of two similar polygons is 3:2, and the area of the smaller polygon is 24 cm2, the ratio of areas of similar figures is the square of the scale factor. This rule can be applied to determine the area of the larger polygon.
To find the area of the larger polygon, first determine the scale factor for the areas by squaring the scale factor for the sides, which is 3:2. The square of 3/2 is 9/4. This means that the area of the larger polygon is 9/4 times the area of the smaller one. Hence, the area of the larger polygon is 24 cm2 × (9/4) = 54 cm2.
Similar polygons demonstrate this principle: their corresponding side lengths, perimeters, and areas increase proportionally. In the given examples, when a square or rectangular side length is doubled, the new area becomes four times that of the original. It's crucial to remember that area is a two-dimensional measurement hence the square of the linear scale factor applies.