The equations of the two adjacent sides of a rhombus are y = x and y = 7x. The diagonals of the rhombus intersect each other at the point (1, 2) then area of the rhombus is

Equation of diagonal AC is  $y-2=\frac{-1}{2}\left(x-1\right)\Rightarrow x+2y=5$
On solving with y = x we get  $A=\left(\frac{5}{3},\frac{7}{3}\right)$
On solving with y = 7x we get   $C=\left(\frac{1}{2},\frac{7}{2}\right)$
Clearly B = (24) required area = $\frac{1}{2}\left|\begin{array}{cc}2& 4\\ \frac{4}{3}& \frac{-2}{3}\end{array}\right|=\left|\frac{1}{2}\times \frac{-20}{3}\right|=\frac{10}{3}$  sq. units