First step I would take, would be to get the rough shape of the exterior rectangle. I'll use orange for contrast purposes:

Next, I'll make the two triangles. They're not equilateral, but I'll get the process started with the Star took and 3 points:

Now I'll align the bottom of it with the rectangle, and distort the top until it aligns with one of the mountains:

Duplicate the triangle by using cmd+c, cmd, shift+v to paste in place. Then, I'll distort this one, making sure it's still aligned with the larger triangle:

I'm going to increase the stroke, and move it out of the way so I can work more accurately:

Now I'll use the pen tool to find the right angle for the right part of the smaller triangle:

Then, I moved the new path onto my illustration in it's correct spot. I Unite it with the smaller triangle:

The rectangle is going to be our most important shape moving forward, so I'll copy it (com+c) before proceeding. I select the large triangle and the rectangle, and Minus Back:

I will Paste in Place the rectangle I copied earlier, select it and the triangle+path we made earlier, and Intersect them:

Going into Outline mode will help us now (com+y). I will add two anchor points on the bottom shape:

Now I can delete the anchor point that's in the way, and move the anchor point on the top shape into a more accurate spot:
Last step! I'll just use the Direct Selection tool and change the radius of the corners until the shape fits:


Now I can add a white shape to create the overlap, and complete the illustration:
