Opencv contour area returns wrong result

I am currently working on a opencv project which determines the contour area. I tried to make a proper threshold and apply cv2.findContours on it. However, I found that when the contour is intersecting the borders of the image, the area is drastically underestimated using cv2.contourArea. How can solve this issue? (Please check the attached images which demonstrates the wrong result on a sample image)

import cv2
import numpy as np

def midpoint(ptA, ptB):
    return ((ptA[0] + ptB[0]) * 0.5, (ptA[1] + ptB[1]) * 0.5)

Input = cv2.imread("Thresh.png")
Thresh = cv2.cvtColor(Input,cv2.COLOR_BGR2GRAY)

contours, hierarchy = cv2.findContours(Thresh,  cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
minArea = 0
for cnt in contours:
    area = cv2.contourArea(cnt)
    print(area)
    if (area > minArea) :
        x,y,w,h = cv2.boundingRect(cnt)
        rect = cv2.minAreaRect(cnt)
        box = cv2.boxPoints(rect)
        box = np.int0(box)
        Input = cv2.drawContours(Input,[box],0,(255,0,0),2)
        (tl, tr, br, bl) = box
        (tltrX, tltrY) = midpoint(tl, tr)
        cv2.putText(Input, "{:1f}".format(area),
        (int(tltrX), int(tltrY)), cv2.FONT_HERSHEY_SIMPLEX,
        0.65, (0, 255, 0), 2)
        cv2.imshow('Input',Input)
cv2.waitKey(0)
cv2.destroyAllWindows()

Input threshold image Determined contours (bounding rectangle) with written contour areas on it