Nico has an outdoor playset in the form of a regular triangular prism covered in a 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
First, let's find the area of each triangular face of the prism.
The formula for the area of a triangle is A = (1/2) * base * height.
Since we are looking for the height of the triangular face, we can rearrange the formula to get height = (2 * area) / base.
The base of the triangular face is the base of the prism, which is 6 ft.
The area of the triangular face is given as 100 ft^2.
Plugging these values into the formula, we have height = (2 * 100) / 6 = 33.33 ft (rounded to 2 decimal places).
Next, let's find the height of the triangular prism.
The slant height is given as 8 ft.
The height of the prism is the height of the triangular face plus the slant height.
So, the height of the prism is 33.33 ft + 8 ft = 41.33 ft (rounded to 2 decimal places).
Therefore, the height of the base to the nearest tenth is 41.3 ft.