Nico has an outdoor play tent in the form of a regular triangular pyramid, covered in fabric on all four sides. The surface area of the tent is 100 ft^2, the base is 6 ft and the slant height is 8 ft. What is the height of the base to the nearest tenth?
The surface area of the triangular pyramid is the area of the base plus the area of the four triangles. The area of the base is $\frac12bh=\frac12(6)(h)$. The area of one of the triangles is $\frac12bh$. Thus, the surface area of the pyramid is $30+4\cdot\frac12(6)h=100$. This gives us $30+12h=100$. Solving for $h$ gives $h = \frac{35}{6}$. Rounded to the nearest tenth, this is $\boxed{5.8}$.
