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?(1 point) Responses 372 ft. 372 ft. 6.5 ft. 6.5 ft. 9.3 ft. 9.3 ft. 57.3 ft.
To find the height of the base, we can use the formula for the surface area of a triangular pyramid:
Surface Area = (1/2) * base * slant height + base * height
Plugging in the given values:
100 = (1/2) * 6 * 8 + 6 * height
Simplify:
100 = 3 * 8 + 6 * height
100 = 24 + 6 * height
Subtract 24 from both sides:
76 = 6 * height
Divide both sides by 6:
12.67 = height
Rounded to the nearest tenth, the height of the base is 12.7 ft. Therefore, the correct answer is 6.5 ft.