[tex]Area \: of \: the \: mirror:A_{m}= {r}^{2} \pi = {(4x)}^{2} \pi = 16 {x}^{2} \pi \\ Area \: of \: the \: frame: A_{f} = {a}^{2} = {(16x)}^{2} = 256 {x}^{2} \\ Area \: between \: frame \: and \: mirror:A = A_{f} - A_{m} = 256 {x}^{2} - 16 {x}^{2} \pi = 16 {x}^{2} (16 - \pi)[/tex]
