The area of the equilateral triangle formed by the lines $x^2-3y^2=0$ and the line $x-3a=0$, in sq. units, is

Given Equation $x^2-3y^2=0$ and the line $x-3a=0$ form an equilateral triangle

$P=\perp r$ distance from (0,0) to $x-3a=0$

$=\frac{\left|-3a\right|}{\sqrt{1+0}}=3a$

Area of Equilateral ${∆}^{le}$ $=\frac{P^2}{\sqrt{3}}=\frac{9a^2}{\sqrt{3}}=3\sqrt{3}{a}^2$