$\mathrm{L}=(2,4)$ and ${\mathrm{L}}^1\left(2,-4\right)$ are ends of latusrectum and P is any point on the directrix of parabola then area of $∆{\mathrm{PLL}}^1$ in sq. units is

$\mathrm{L}=(2, 4) \& {\mathrm{L}}^1=(2, -4)$ 

Since x-coordinates are equal then axis is symmetric to x -axis.

$$\begin{gathered} LL\text{'}=8 \\ \Rightarrow 4\mathrm{a}=8 \\ \Rightarrow a=2 \end{gathered}$$ 

  focus$=(2, 0) (\mathrm{h}, \mathrm{k})=(0,0)$

base of triangle $4=4\mathrm{a}=8$ 

point on directrix is $\left(-\mathrm{a}+\mathrm{h}, \mathrm{k}\right)=\left(-2, 0\right)$

height$=\sqrt{{\left(4\right)}^2+0}=4$

$∆=\frac{1}{2}$ (base$\times$height)

    $$\begin{gathered} =\frac{1}{2}\times 4\mathrm{a}\times 4 \\ =\frac{1}{2}\times 8\times 4 \\ =16 \mathrm{sq}.units \end{gathered}$$