helps.

Not as hard as  it seems

We have  a rectangle with an area  of  Width * Height  = 34 * 14  = 476  units^2     (1)

Note...that at the two ends, we have two semi-circles with a radiuses of 7 

So...the total area of these combined will actually be a circle with a radius of 7  = pi * 7^2  = 49pi units^2   (2)

So the shaded area  =  (1)  - (2)  =  476  - 49pi  ≈   322.1  units^2