2023 AMC 10B Problems/Problem 25
Problem
A regular pentagon with area 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?
Solution 1
Let and
be the circumradius of the big and small pentagon, respectively. Let
be the apothem of the smaller pentagon and
and
be the areas of the smaller and larger pentagon, respectively.
From the diagram:
~Technodoggo