The "Ball Box" problem

The Acme Tennis Ball Company is designing a new box to ship its products. The marketing department wants a triangular box that can hold 4 balls, as in the illustration below. The balls fit exactly inside the box, just touching all three walls and the end caps of the container. All 3 walls of the box are the same size.

Assume a tennis ball is 6 cm in diameter, and ignore the thickness of the box material.

Problem 1
The end of the box is in the shape of a triangle.
What is the type and dimensions of the triangle to 2 decimal places? show answer
An equilateral triangle whose sides are 10.39 cm.
Challenge problem 2
Calculate, to 2 decimal places, the surface area of the box, including the two end caps. show answer
841.75 cm2 (end caps: 46.765 each, side walls 249.408 each)

Resources (and perhaps clues)