A pole 10 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Suav measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.

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.