A thresholded image may be derived by setting all pixels below a certain value, the threshold, to 1 and all others to 0 (these values, 0 and 1, may be reversed depending on the application). A threshold value may be selected by trial and error, but a better way is the look at the histogram of the image to pick a reasonable value.
Here is the above image thresholded at pixel value 15 and below:
In the above threshold image the pixels less than or equal to 15 were set to one and colored blue. All other pixels were set to one and colored pale orange.
The number of pixels of values 0 through 15 is 8598, as found by adding up all the values in the thresholded image (that's way the desired pixels were set to 1 and all others to 0). Each pixel was previously determined to be 28.5 by 28.5 meters, so the area of a pixel is about 812 square meters. The total area of Liberty Reservoir as measured in band 5 of this image (using pixel values up to 15) is 8598*28.5^2 = 6.9837e6 sq meters. One sq Km = 1e6 sq m, so the area is 6.98 sq Km or about 2.7 sq miles.
The same area may be found by histogramming the image and counting the pixels at or below the threshold value.
Which technique is better? They are equivalent but viewing the thresholded image verifies that almost all the selected pixels are actually part of Liberty Reservoir. It also shows that a few pixels of water are covered up by several bridges. If it is known ahead of time that the image divides cleanly into two distinct areas then the histogram technique has value for automating the area measurement process.