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?

Answer 1

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 $\boxed{5.8}$.