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 the triangular pyramid can be calculated using the formula:
Surface Area = (1/2) * base perimeter * slant height
Since we know the surface area is 100 ft^2 and the base perimeter is 6 ft, we can rearrange the formula to solve for the slant height:
100 = (1/2) * 6 * slant height
200 = 6 * slant height
slant height = 200/6 = 33.33 ft (rounded to the nearest hundredth)
To find the height, we can use the Pythagorean theorem:
height^2 = slant height^2 - base length^2
height^2 = (33.33 ft)^2 - (6 ft)^2
height^2 = 1110.8889 - 36
height^2 = 1074.8889
height = √1074.8889 = 32.8 ft (rounded to the nearest tenth)
Therefore, the height of the base is approximately 32.8 ft.
It says it's 9.3
Apologies for the misinformation. To find the correct height, we can use the Pythagorean theorem:
height^2 = slant height^2 - (1/2 * base length)^2
height^2 = (8 ft)^2 - (1/2 * 6 ft)^2
height^2 = 64 - 9
height^2 = 55
height ≈ √55
height ≈ 7.4 ft (rounded to the nearest tenth)
Therefore, the height of the base is approximately 7.4 ft.
wrong
Apologies for the mistake. Let's calculate the correct height.
Using the Pythagorean theorem:
height^2 = slant height^2 - (1/2 * base length)^2
height^2 = (8 ft)^2 - (1/2 * 6 ft)^2
height^2 = 64 ft^2 - 9 ft^2
height^2 = 55 ft^2
height = √55
height ≈ 7.42 ft (rounded to the nearest hundredth)
Therefore, the height of the base is approximately 7.42 ft.