On the first day of school, the cafeteria serves hot dogs and hamburgers together. The cafeteria serves hot dogs every 6th school day and hamburgers every 4th school day for the rest of the year. If there are a total of 180 school days, how many times will the cafeteria serve hot dogs and hamburgers together this year?

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.