least square root fit with piecewise function

I would like to perform a fit with a piecewise function, but the curve fitting app doesn't allow that. I have 102 points (see the figure), and I think they could fit nicely with 2 lines. mind that the plot is bi-logaritmic and I want to impose the least square root in the linear space. I also would like to impose a constraint on the area under the fitting curve. I tried to use lsqcurvefit but it converges very slowly. I used those options

options = optimoptions('lsqcurvefit','Algorithm','trust-region-reflective',...
            'PrecondBandWidth',0,'SubproblemAlgorithm','cg','MaxFunEvals',4*10^5,'MaxIter',4*10^5,'TolFun',10^-25, ...
            'StepTolerance', 10^-10);

and it took those times (to reach the stop criteria) %%'MaxFunEvals',4*10^5,'MaxIter',4*10^5 it takes 327 %%'MaxFunEvals',4*10^5,'MaxIter',4*10^5 it takes 278 'cg' %%'MaxFunEvals',4*10^5,'MaxIter',4*10^5 it takes 137 'cg' PrecondBandWidth 0 %%'MaxFunEvals',4*10^6,'MaxIter',4*10^5 it takes 1100 %%'MaxFunEvals',4*10^6,'MaxIter',4*10^5 it takes 410 'cg' PrecondBandWidth 0 when I say that the solution moves a little, I mean that from x1=4.0*10^5 in the last example it converges at 3.90*10^5

what can I do?