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Answer :
Final answer:
The ratio of the areas of two similar pentagons is the square of the ratio of their corresponding sides. With a side length ratio of 3/4 to 2/3, the area ratio of the larger pentagon to the smaller pentagon is 81:64.
Explanation:
We use the fact that when two shapes are similar, the ratio of their areas is the square of the ratio of their corresponding sides. In this case, the larger pentagon has a side length of 3/4 and the smaller pentagon has a side length of 2/3. To find the ratio of their areas, we calculate (3/4)^2 / (2/3)^2 = (9/16) / (4/9) = 81/64. Therefore, the ratio of the area of the larger pentagon to the area of the smaller pentagon is 81:64.
If you know the scale factor of two similar polygons, you can find the perimeter of the second polygon by multiplying the perimeter of the first polygon by the scale factor. The area of the second polygon is found by multiplying the area of the first polygon by the scale factor squared.
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