The parent function of a quadratic, f(x) = x^2 is reflected across the x-axis, vertically compressed by a factor of 5/11, translated 15 units left and 4 units down. Write the equation of the transformed quadratic function, g(x), in vertex form.

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.