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?
The surface area of a regular triangular pyramid is given by the formula:
Surface Area = (base perimeter x slant height) / 2
The base perimeter can be calculated by multiplying the length of one side of the base by 3, as there are three sides in a regular triangular pyramid.
Base perimeter = 6 ft * 3 = 18 ft
Plugging in the given values into the formula for surface area, we get:
100 ft.2 = (18 ft x 8 ft) / 2
Multiplying both sides by 2, we get:
200 ft.2 = 18 ft x 8 ft
Dividing both sides by 18 ft, we get:
Height = 200 ft.2 / 18 ft = 11.1 ft
Therefore, the height of the base of the tent is approximately 11.1 feet.
57.3 ft
9.3 ft
375 ft
6.5 ft
To find the height of the base, we can use the formula for the surface area of a triangular pyramid:
Surface Area = (base perimeter x slant height) / 2
Plugging in the given values, we have:
100 ft^2 = (base perimeter x 8 ft) / 2
Simplifying the equation, we have:
200 ft^2 = base perimeter x 8 ft
To determine the base perimeter, we can divide 200 ft^2 by 8 ft:
base perimeter = 200 ft^2 / 8 ft = 25 ft
Since the base is in the form of a regular triangle, we can divide the base perimeter by 3 to find the length of one side of the base:
side length = 25 ft / 3 = 8.3 ft
To find the height of the base, we can use the Pythagorean Theorem:
(h)^2 = (slant height)^2 - (base/2)^2
(h)^2 = 8 ft^2 - (8.3 ft / 2)^2
(h)^2 = 8 ft^2 - 17.22 ft^2
(h)^2 = -9.22 ft^2
Since the height cannot be negative, the solution is not valid. Therefore, the given values are incorrect or do not correspond to a regular triangular pyramid with the surface area provided.