# how can I calculate covered area under a single-slope roof?

I'm looking to build a small covered patio area on our property, next to our pool. It'll be open on all sides, and covered by a simple skillion/single-sloped roof. So something like in this photo:

http://fancycribs.com/wp-content/uploads/2011/03/Broadford-Farm-Pavilion-LakeFlato-Architects-600x402.jpg

The idea behind the single sloped roof is that we'd like to be able to put a bunch of PV panels up there to generate some solar energy.

So my question is this: how can I combine the roof dimensions, with the angle/pitch of the roof, to determine the amount of area that will actually be covered? Suppose the roof is 20 feet long by, say, 15 feet wide. If it were flat that would be easy. But if the roof is angled at say, 30 degrees, then that will change the actual area of the space below that the roof actually covers. How would I go about calculating that exactly? I'm really not even sure where to start on something like this.

Any help would be greatly appreciated. Thanks!

• Many ways. Ways involving trig, Geometry, and even calculus come quickly to mind. What do you already know? I would say a trig-geometry blend would be the cleanest approach – Brevan Ellefsen Mar 28 '16 at 1:17
• – Tester101 Mar 28 '16 at 13:36