Step-by-step explanation:
[tex] {x}^{2} = 2 \times {4}^{2} \\ {x}^{2} = 32 \\ x = 4 \sqrt{2} \\ diameter = 4 \sqrt{2} \\ radius = 2 \sqrt{2} \\ area \: of \: half \: of \: the \: circle = \\ [/tex]
[tex]a = \frac{\pi \times {(2 \sqrt{2} )}^{2} }{2} = 4\pi \\ area \: of \: triangle \: = \\ 2 \sqrt{2} \times 2 \sqrt{2} = 8 \\ area \: of \: shaded \: region \: is \: = \\ 4\pi - 8 = 4.57 \: {cm}^{2} [/tex]
