Will these table legs be able to support this table design or will they need additional supporting features? I'm specifically talking about the structural integrity of the legs, seeing as how they are angled. The "V" is secured to the table and bottom portion using two Biscuits at each joint. The wood is Red Cedar (too soft, I know).
There are cross braces in place parallel to the short ends under the table. They are 5 of them evenly spaced out.
I apologize for the poor sketchup quality.
That design will have problems with racking forces (based on what I can see from the point of view you show1). If I stand at the end of the table and push wilh a little force the legs would probably break from the table top.
Table have aprons and/or stretchers to help mitigate this. You need something to brace the legs. Take a look at this shaker style table. It was the first one I found that showed some detail under the top.
Image from mjolk.ca
Shaker style (the ones that look like above at least) doesn't use stretchers which keeps more free space under the table . That is an aesthetic choice and you could easily have a couple of stretchers connecting the opposite table legs.
The legs as they are now on their own should be fine however I would op for mortise and tenon joinery for your legs for both the table end and feet. That would make the leg assembly more stable. As long as part of the frame (that is not the table top) connects the legs it should be OK.
1 Using Xray view in SketchUp is one way to show us under the top without having to provide two pictures
Will these table legs be able to support this table design or will they need additional supporting features?
Going by the additional detail provided in your Comment, I'm fairly sure that's enough support.
The "V" is secured to the table and bottom portion using two Biscuits at each joint.
This is your major design concern here, if I'm interpreting your intention correctly. It's important not to rigidly affix solid-wood tabletops to leg assemblies as it constrains seasonal movement — the wood of the tabletop must be free to expand and contract as its moisture content goes up and down through the year (a natural cycle, related to the humidity in the environment).
Instead of using biscuits it would be better to attach the tabletop to the cross supports using hardwood buttons (left), or more simply, expansion plates (right):
Note there are numerous other metal fastener options for attaching tabletops, I'm a fan of the above type as they are the simplest to install; they are also sold as "table stretcher plates" in case that helps in locating a source.
