The equation of one side of a rectangle is $3x-4y-10=0$ and the coordinates of two of its vertices are $(-2,1)$ and $(2, 4)$.Then,  the area of the rectangle, in square units, is 

 

We observe that none of the vertices $A(-2,1)$ and 

$B(2,4)$ ) lie on the side $3x-4y-10=0$. Therefore,

Length of one side of the rectangle is 

$AB=\sqrt{(-2-2{)}^2+(1-4{)}^2}=5$

Also,

 Length of the other side

= Length of the perpendicular drawn from $A(-2,1)$ on

$3x-4y-10=0$

$=\left|\frac{-6-4-10}{\sqrt{9+16}}\right|=4$

$\therefore$       Area of the rectangle =  5 x 4 = 20 sq. units