It will not give a very accurate result, but when calculating pool volumes, the typical approximation is to just take the average of the deep end and the shallow end and use that as the depth throughout. Usually the result is used for deciding how much chlorine or algaecide to put in, and a very rough estimate is good enough.
So, the depth is (6+3.5)/2 = 4.75 feet.
The area is (10.5*8) + (7*1) + (12*6) +(15*16) = 403 square feet.
So the volume is (403 square feet)*(4.75 feet) = 1914.25 cubic feet, and the conversion rate is 7.48 gallons per cubic foot, so the calculation comes out to 14318.59 gallons. So you can probably use 15,000 gallons for the volume.
If you need a more accurate result, measure the depth at the start and end of each of the four rectangles and multiply the average for each rectangle by the area of the rectangle. If the bottom slopes evenly from one side of the rectangle to the other, that should give a really accurate result.