A farmer in Kenya sketches the edge of a field as the curve $y = 16 - x^2$ and covers the region under it with four rectangles of width $1$ metre, as in the figure. The top right corner of each rectangle touches the curve, and the last rectangle has height $0$. What is the total area of the four rectangles, in square metres?

Fig. 1: The blue curve y = 16 - x squared for x from 0 to 4, falling from height 16 to 0. Four orange rectangles of width 1 stand on the x-axis, one on each of the intervals from 0 to 1, 1 to 2, 2 to 3 and 3 to 4. The top right corner of each rectangle touches the curve, so the rectangles lie below it. The last rectangle has height 0.