Carlos downloaded a pattern from the Internet for making a table with an irregular polygon-shaped top. The instructions on the pattern say that the
scale factor is 11/2. The sides of the pattern are shown on the diagram below.
What is the length of the longest side of the finished tabletop?

A3cm×3cm\greend{3\,\text{cm} \times 3\,\text{cm}} 3cm×3cm start color greend, 3, space, c, m, times, 3, space, c, m, end color greend rectangle sits inside a circle with radius of 4cm\blued{4\,\text{cm}} 4cm start color blued, 4, space, c, m, end color blued . what is the area of the shaded region? round your final answer to the nearest hundredth.