For this item, any non-integer answers should be entered as decimals, rounded to the hundredths place.
Jade wanted to know if she could fit her watches in the box below. The box is in the shape of a rectangular prism.
The length of diagonal DG is approximately ___cm.
The length of diagonal AG is approximately ___ cm.

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.