Help getting an equation for the area of this shape

So the shape is like a rectangular base with a semi-circle on top of that rectangle. In such a way that the base of the rectangle is 2r. The perimeter is 40cm.

https://www.google.co.uk/search?hl=en&q=rectangle+with+semicircle+on+top&bav=on.2,or.r_qf.&bvm=bv.46751780,d.d2k&biw=1366&bih=667&pdl=300&um=1&ie=UTF-8&tbm=isch&source=og&sa=N&tab=wi&ei=uUSXUbCzOIem4gTygIGACA#imgrc=PxwhGU0nw--RzM%3A%3BaRH1W1Rz2sgT8M%3Bhttps%253A%252F%252Fassessment.casa.uh.edu%252FAssessment%252FImages%252F%252F1750457.gif%3Bhttp%253A%252F%252Fwww.chegg.com%252Fhomework-help%252Fquestions-and-answers%252Ffigure-shows-region-consists-semi-circle-rectangle-value-x-maximizes-area-region-circumfer-q1375398%3B248%3B258 like that.

Show that A=40r - 2r^2 - (pi*r^2)/2.

I began by calling h the height of the rectangle part and setting:

2rd+pi*r = 40.
Then I thought maybe I could do an equation for the area of the triangle, make h the subject of that equation and substitute that into the equation stated above. So I tried but can't really do it.

Any suggestions?