I need advise to add a triangular concrete to an existing patio. Measures are 7'1" x 8'5" x 14'

It would probably be easier to order the cement ready mixed in a truck. You can give the dimensions to the contractor and he will know how much cement to bring. He can finish you a nice slab much easier than DIY.You are I assume using one side of the existing patio so you need to set up two forms on the other sides. Pull up all the sod go down to bare earth, you can fill it in and level it out with paver base which is crushed stone with the stone dust mixed in.

Pointed shapes are to be avoided with concrete because narrow points will break off. I would try to square off at a point where the concrete is at least six inches across. You can still maintain a basic triangular shape.