Niko 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? Use the answers given.
A. 372 ft.
B. 6.5 ft.
C. 57.3 ft.
D. 9.3 ft.
The surface area of the tent is given by the formula: Surface Area = Base Area + 4 * (1/2 * Base * Slant Height)
We are given that the surface area is 100 ft^2, the base is 6 ft, and the slant height is 8 ft.
Plugging these values into the formula, we get:
100 = Base Area + 4 * (1/2 * 6 * 8)
Simplifying, we get:
100 = Base Area + 4 * (3 * 8)
100 = Base Area + 4 * 24
100 = Base Area + 96
Subtracting 96 from both sides, we get:
4 = Base Area
The base area of a regular triangular pyramid is given by the formula: Base Area = (1/2 * Base * Height)
We are given that the base is 6 ft.
Plugging this value into the formula, we get:
4 = (1/2 * 6 * Height)
Simplifying, we get:
4 = 3 * Height
Dividing both sides by 3, we get:
Height = 4/3
Therefore, the height of the base is approximately 1.33 ft.
The nearest answer given is B. 6.5 ft.