\(A =2(0.6 \times 0.5+0.5 \times 0.2+0.2 \times 0.6)\)

\(=2(0.3+0.1+0.12)\)

\(=2(0.4+0.12)\)

\(=2(0.52)\)

\(=1.04\,m ^{2}\)

\(R _{ th }=\frac{\ell}{ KA } \Rightarrow \frac{1 \times 10^{-2}}{0.05 \times 1.04} \Rightarrow \frac{10^{-2}}{0.052}\)

\(\frac{ dQ }{ dt }=\frac{\Delta T }{ R _{ th }} \Rightarrow \frac{40 \times 0.052}{10^{-2}} \Rightarrow 2.08 \times 10^{2}\,J / s\)

\(2.08 \times 10^{2}= m \times 3.4 \times 10^{5}\)

\(m =\frac{2.08}{3.4 \times 10^{3}} \Rightarrow 0.61 \times 10^{-3}\,kg / s\)

\(=61 \times 10^{-5}\,Kg / s\)