a regular pentagon with area 1 5 is printed on paper and cut out. all five vertices are folded to the center of the pentagon, creating a smaller pentagon. what is the area of the new pentagon?

The area of the new pentagon will be proportionally smaller than the original pentagon, in direct proportion to the square of the scaling factor between the two pentagons.

Explanation:

The question asks for the area of a new, smaller pentagon formed by folding the vertices of a regular pentagon with an area of 1.5 to its center. This action reduces the size of the pentagon while maintaining its regularity and proportionality.

Using properties of similarity and considering that each side of the smaller pentagon is now a portion of the sides of the original pentagon, the area of the similar and smaller pentagon would also be reduced proportionally.

However, we can conclude qualitatively that the smaller pentagon will have a smaller area than the original pentagon, and the area will be in direct proportion to the square of the scaling factor between the sizes of the two pentagons.

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