How do I find the area of multiple shaded rectangles in a parabola? It's most easily explained if you look at this image (sorry for the bad quality!): 
I haven't drawn it too well, the vertex should be at the y-axis.
I'm not sure how to find the area of the shaded region. The height is variable, and I've got an equation for the parabola based on h. The width of each rectangle is 2.5.
It's very similar to Riemann sums, but horizontal. I thought about using a series, but I'm not sure how.
Any ideas?
Cheers!
EDIT: I should have been more specific. I do know how to find the total area of the shaded region for a specific height, say h=36. However, I'm trying to generalize a function f(h) where I plug in h, and it spits out the total shaded area.

Let me call the height of each rectangle $2.5$. Note that the top of the bottommost rectangle intersects the $y$-axis at $y=2.5$. 
Note that the top right corner of this rectangle coincides with the point on the parabola with coordinates, say, $(  x_1, 2.5)$. So,
half the width of this rectangle is $x_1$ and can be obtained by finding the positive solution to:
$$
2.5= {-h\over 36^2}\cdot x_1^2+h 
$$
This gives $$\tag{1}x_1=\sqrt{36^2( h-2.5)\over h }.$$
So, the width of the bottommost rectangle is $2x_1$, and its area is $(2.5)\cdot 2x_1=5x_1$.
The top of the second rectangle from the bottom intersects the $y$-axis at $y=5$ and the top right corner of this rectangle coincides with the point on the parabola with coordinates, say, $(  x_2, 5)$. You may argue as above to find its width (note that to find half the width, you may just take equation (1) and replace "2.5" by "5" and $x_1$ with $x_2$"), then its area.
Continue for each rectangle and then take the sum.  Note that the number of rectangles is the integer part of $h/2.5$
