Answer
$ 204.16 m^{2}$
Work Step by Step
$y=4$
$rsin\theta=4$
$r=\frac{4}{sin\theta}$
$\frac{4}{sin\theta}=8+8sin\theta$
$\theta=arcsin\frac{-1+\sqrt 3}{2}$ $\approx 0.374734$ radians or $21.47 ^\circ $
$\theta=arcsin\frac{-1-\sqrt 3}{2}$
$=arcsin(-1.3660254)$
$A=2\int_{0.374734}^{\pi/2}(\frac{1}{2})((8+8sin\theta)^{2}-(\frac{4}{sin\theta})^{2}d\theta$
$=16[3\pi-(-3.33522)]$
$\approx 204.16 m^{2}$
