Raised triangular decking

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I'm an electrical engineer by trade, so do excuse my ignorance when it comes to woodwork, however...

I'd like to build a raised deck in the corner of my garden. Currently the majority of the area I'd like to cover is paved, although the paving isn't particularly level and ideally I'd like to remove it, lay down some weed proof membrane, cover with chippings or bark and then build the deck above this on supports.

The area I want to deck is a 5.6 by 3.3 metre right angle triangle. For lack of a better way to describe it, I'd like to build the deck the shape of a triangle with the two non right-angle corners filed down.

I can visualise how I'd support a rectangular deck above ground level, but don't know where to start with a triangle. Clearly there will have to be some framework to support the deckboards, and preferably as few supports as possible to avoid digging a large number of holes. Given the angles that would be involved in constructing this shape, what would be the best way to attach the framework together?

My initial thoughts would be to mitre the framework, butt the supports up to each other and screw them together. Given further thought, this doesn't seem such a great idea with a raised deck as I don't think this sort of joint would provide enough strength.

Hopefully most of that made sense, although if you need a drawing of the shape I'm trying to build then just give me a shout. What I really want to know is how the framework for irregular shapes would normally be constructed, I've seen it done before plenty of times so there must be a secret to it!

Thanks in advance

Matthew

EDIT: I also should have mentioned that I'm planning on having a balustrade around the edges, so it would make sense for the supports to be positioned accordingly to support it.
 
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