Ratio of areas

$\text{Area of x = Area of rectangle - Area of half circle}\\ x=(r\times 2r)-(\frac { \pi }{ 2 } r^{ 2 })=r^{ 2 }(2-\frac { \pi }{ 2 } )\\ \text{Area of y = Area of equilateral triangle} - 3\times \color{#3D99F6} (\frac { 1 }{ 6 } \text{Area of circle}) \text{//sector with angle 60°}\\ y=\frac { \sqrt { 3 } }{ 4 } (2r)^{ 2 }-\frac { \pi }{ 2 } r^{ 2 }=r^{ 2 }(\sqrt { 3 } -\frac { \pi }{ 2 } )\\ \text {Area of shaded }= 8x+10y=r^{ 2 }(16+10\sqrt { 3 } -9\pi )\\ \text {Area of unshaded} = 10\times Area of circle=r^{ 2 }(10\pi )\\ \\ \text {the ratio} =\frac { r^{ 2 }(16+10\sqrt { 3 } -9\pi ) }{ r^{ 2 }(10\pi ) } =\frac { 16+10\sqrt { 3 } -9\pi }{ 10\pi } \approx 0.16$