A yacht leaves port P and travels 34km due north to an island I. At I, the yacht turns on a bearing of 054° from I and travels a further 48km until it reaches marker buoy B. At B, the yacht turns again and travels back in a straight line to P. Calculate the total distance travelled by the yacht, to the nearest kilometre.

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.