The formula for the surface area of a regular triangular pyramid is given by:
Surface Area = base area + lateral area
The base area of a regular triangular pyramid is given by:
Base area = (1/2) * base * height
And the lateral area is given by:
Lateral area = (1/2) * perimeter * slant height
Given that the surface area is 100 ft^2, the base is 6 ft, and the slant height is 8 ft, we can set up the equation:
100 = (1/2) * 6 * height + (1/2) * perimeter * 8
Since it is a regular triangular pyramid, the perimeter is equal to 3 times the base. Therefore, we have:
100 = (1/2) * 6 * height + (1/2) * 3 * 6 * 8
100 = 3 * height + 3 * 6 * 8
100 = 3 * height + 144
Subtracting 144 from both sides gives:
-44 = 3 * height
Dividing both sides by 3 gives:
-44/3 = height
Therefore, the height of the base to the nearest tenth is -14.7 ft. However, since the height of a pyramid cannot be negative, we can conclude that the given values for the surface area, base, and slant height do not form a valid triangular pyramid. Therefore, none of the provided options (6.5 ft, 57.3 ft, 372 ft, or 9.3 ft) is correct.
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
6.5 ft.
6.5 ft.
57.3 ft.
57.3 ft.
372 ft.
372 ft.
9.3 ft.
3 answers
pick one
6.5 ft.