Area (A) $=5\mathit{c}\mathit{m}\times 8\mathit{c}\mathit{m}=40\mathit{c}{\mathit{m}}^2$
$=40\times {10}^{-4}{\mathit{m}}^2=4\times {10}^{-3}{\mathit{m}}^3$
The loop lies in the x-y plane, so its area vector is along the z-direction $\left(\stackrel{\wedge }{\mathit{k}}\right)$.
The magnetic field is given as $\overrightarrow{\mathit{B}}=2.0\stackrel{\wedge }{\mathit{k}}$.
Since $\overrightarrow{\mathit{B}}$ and $\overrightarrow{\mathit{A}}$ are parallel, $\mathit{\theta }=0\circ$ and $\mathit{c}\mathit{o}\mathit{s}\mathit{\theta }=1$.
$\mathit{\phi }=\mathit{B}\times \mathit{A}=2.0\times \left(4\times {10}^{-3}\right)=8\times {10}^{-3}\mathit{W}\mathit{b}$
The total magnetic flux is $8\times {10}^{-3}\mathit{W}\mathit{b}.$