Nico has an outdoor play tent in the form of a regular triangle pyramid covered in fabric on all four sides. The surface area of the tent is 100 feet the base is 6 feet and the slant height is 8 feet. What is the height of the base to the nearest 10th.
The surface area of a regular triangle pyramid is given by the formula:
Surface Area = (base perimeter)*(slant height)/2
Since we know the surface area is 100 feet and the base is equilateral with a length of 6 feet, the perimeter is 3 times the length of the base, which is 3*6 = <<3*6=18>>18 feet.
Substituting these values into the formula, we get:
100 = (18)*(8)/2
Simplifying, we get:
100 = 144/2
100 = 72
This is a contradiction, so the equation has no solution.
Therefore, there is no height of the base that satisfies the given conditions.