$\beta_1-\beta_2=10 \log \frac{I_1}{I_2}$

$6=\log \frac{I_1}{I_2}$

$I_2=10^{-6} I_1$

$I = I _0 e ^{-\alpha / 4}$

$10^{-6} I _0= I _0 e ^{- a / 4} \Rightarrow \alpha=24 \ln 10$

Using dimensional analysis we get

$\alpha=\frac{ A _{ e } V _{ s } t }{ V }$

[Although it cannto be calculated technically, as we have less equations and more variables but this is done just by observation]

$24 \ell \operatorname{n} 10=\frac{ A _{ e } v _{ s } t }{ v }$

$A _{ e }=\frac{24 \ell n 10 \times v }{ v _{ s } t }$

$A _{ e }=\frac{24 \times 6400 \times 2.303}{340 \times 1}$

$A _{ e }=97.6 \approx 100 \,m ^2$