A \greenD{3\,\text{cm} \times 2\,\text{cm}}3cm×2cmstart color #1fab54, 3, start text, c, m, end text, times, 2, start text, c, m, end text, end color #1fab54 rectangle sits inside a circle with radius of \blueD{4\,\text{cm}}4cmstart color #11accd, 4, start text, c, m, end text, end color #11accd. What is the area of the shaded region? Round your final answer to the nearest hundredth.

Acompany manufactures three types of cabinets. it makes 110 cabinets each week. in the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. the next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.