A loop, made of straight edges has six comers at A(0, 0, 0), B(L, 0, 0) c(1, L, 0), D(0, L,-0), E(0, L, L) and F(0,0, L). A magnetic field $\mathrm{B}={\mathrm{B}}_0(\widehat{\mathrm{i}}+\widehat{\mathrm{k}})$ Tesla is present in the region. The flux passing through the loop ABCDEFA (in that order) is

The loop can be considered in two planes :
 

(i) Plane of ABCDA is in X-Y plane. So its vector 
$\overrightarrow{\mathrm{A}}$ is in Z-direction. Hence,
${\mathrm{A}}_1=\left|\mathrm{A}\right|\widehat{\mathrm{k}}={\mathrm{L}}^2\widehat{\mathrm{k}}$
(ii) Plane of DEFAD is in Y-Z plane
So A, $=\left|\mathrm{A}\right|\widehat{\mathrm{i}}={\mathrm{L}}^2\widehat{\mathrm{i}}$
$\begin{array}{l}\therefore \mathrm{A}={\mathrm{A}}_1+{\mathrm{A}}_2={\mathrm{L}}^2(\widehat{\mathrm{i}}+\widehat{\mathrm{k}})\\ \mathrm{B}={\mathrm{B}}_0(\widehat{\mathrm{i}}+\widehat{\mathrm{k}})\end{array}$
so, Q = B.A $={\mathrm{B}}_0(\widehat{\mathrm{i}}+\widehat{\mathrm{k}})\cdot {\mathrm{L}}^2(\widehat{\mathrm{i}}+\widehat{\mathrm{k}})={\mathrm{B}}_0{\mathrm{L}}^2$ 
$[\widehat{\mathrm{i}}\widehat{\mathrm{i}}+\widehat{\mathrm{i}},\widehat{\mathrm{k}}+\widehat{\mathrm{k}}\widehat{\mathrm{i}}+\widehat{\mathrm{k}},\widehat{\mathrm{k}}]$
$\begin{array}{l}={\mathrm{B}}_0{\mathrm{L}}^2[1+0+0+1]\left(\therefore \cos {90}^{\circ }=0\right)\\ =2{\mathrm{B}}_0{\mathrm{L}}^2\mathrm{Wb}\end{array}$