Verify Median Value with Area Under the Curve Calculation

I want to calculate the area under this curve for confirmation that the size is correct. How would one go about doing this?

I have a frequency plot below. The package utilized for this median calculation is here: https://github.com/nudomarinero/wquantiles

def annot_median(Size,Count, ax=None):
    xmedian = weighted.median(Size, Count)
    ymedian = np.interp(xmedian,Size, Count)
    text="median " + "[{:.2f},{:.0f}]".format(xmedian, ymedian)
    if not ax:
        ax=plt.gca()
    bbox_props = dict(boxstyle="square,pad=0.3", fc="w", ec="k", lw=0.72)
    arrowprops=dict(arrowstyle="->",connectionstyle="angle,angleA=0,angleB=85")
    kw = dict(xycoords='data',textcoords="axes fraction",
              arrowprops=arrowprops, bbox=bbox_props, ha="right", va="top")
    ax.annotate(text, xy=(xmedian, ymedian), xytext=(0.94,0.86), **kw)
    
annot_median(Size,Count)

I started with thinking the trapezoid method could be utilized to verify that value

x = Size
y = Count 
Area_t=np.trapz(x[:],y[:])

How can I write something so when Area_t = 0.5(total) print corresponding x and y values??

Answer