Question

The plane $4x+4y+8z=16$ meets the coordinate axes $x,y$ and $z$ at $A,B$ and $C$ respectively. Then the area of the $\Delta ABC$ is equal to $k\sqrt{6}.$ The value of k is

Answer 1

Coordinates of $A,B$ and $C$ is $(4,0,0),(0,4,0)\text{and}(0,0,2)$ respectively.



From the above figure,
$△ABC$ is isosceles triangle in which $AC=BC$
Let $D$ be the mid point of $AB$
$\therefore D\equiv (2,2,0)$
$CD=2\sqrt{3},AB=4\sqrt{2}$
So, the area of $△ABC$$=\frac{1}{2}\times CD\times AB=4\sqrt{6}$