Answer
About 11.46 inches
Work Step by Step
The height is equal to the altitude of the equilateral triangle in the center plus 2 radius (one on the bottom and one on the top.)
Altitude=.5(4)$\sqrt 3$
A=2$\sqrt 3$
h=A+2r
h=8+2$\sqrt 3$
h$\approx$11.46
