The surface area of a triangular pyramid is given by the formula:
Surface area = base area + lateral area
The base area of a regular triangular pyramid is given by the formula:
Base area = (1/2) * base * base to height ratio
The lateral area of a regular triangular pyramid is given by the formula:
Lateral area = (1/2) * perimeter * slant height
First, let's calculate the base area:
Base area = (1/2) * 6 ft * (base to height ratio)
Next, let's calculate the lateral area:
Lateral area = (1/2) * (perimeter) * 8 ft
Since we know the lateral area and the base area, we can solve for the base to height ratio:
100 ft^2 = (1/2) * 6 ft * (base to height ratio) + (1/2) * (perimeter) * 8 ft
100 ft^2 = (1/2) * 6 ft * (base to height ratio) + (1/2) * (3 * 6 ft) * 8 ft
100 ft^2 = (3 ft * base to height ratio) + (36 ft * 4)
100 ft^2 = 3 ft * base to height ratio + 144 ft
100 ft^2 - 144 ft = 3 ft * base to height ratio
-44 ft = 3 ft * base to height ratio
Dividing both sides by 3 ft gives:
-44 ft / 3 ft = base to height ratio
base to height ratio = -14.6667 ft
Since the base to height ratio is negative, this implies that the pyramid is inverted. However, because the problem states that the tent is in the form of a regular triangular pyramid, we can conclude that there was an error in the calculations above.
From the given options, none of them are reasonable or 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 100ft.^2 , the base is 6 ft., and the slanted height is 8 ft. What is the height of the base to the nearest tenth? (1 point)
372 ft.
57.3 ft.
9.3 ft.
6.5 ft.
1 answer