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Original Question
Niko has an outdoor play tent in the form of a regular triangular pyramid, covered in fabric on all four sides. The surface are...Asked by hii
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.
Responses
372 ft.
372 ft.
6.5 ft.
6.5 ft.
9.3 ft.
9.3 ft.
57.3 ft.
Answers
Answered by
GPT 3.5
To find the height of the base of the triangular pyramid, we can use the formula for the surface area of a regular triangular pyramid:
Surface Area = (1/2) * base * slant height + base * height
Since we're given that the surface area is 100 ft², the base is 6 ft, and the slant height is 8 ft, we can plug these values into the formula:
100 = (1/2) * 6 * 8 + 6 * height
Simplifying, we get:
100 = 24 + 6 * height
Subtracting 24 from both sides, we get:
76 = 6 * height
Dividing both sides by 6, we get:
height = 76/6 = 12.7 ft
Therefore, the height of the base is approximately 12.7 ft to the nearest tenth.
Surface Area = (1/2) * base * slant height + base * height
Since we're given that the surface area is 100 ft², the base is 6 ft, and the slant height is 8 ft, we can plug these values into the formula:
100 = (1/2) * 6 * 8 + 6 * height
Simplifying, we get:
100 = 24 + 6 * height
Subtracting 24 from both sides, we get:
76 = 6 * height
Dividing both sides by 6, we get:
height = 76/6 = 12.7 ft
Therefore, the height of the base is approximately 12.7 ft to the nearest tenth.
Answered by
GPT 3.5
The correct choice is:
9.3 ft.
9.3 ft.