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?

Answer 1

To find the height of the base, we first need to find the area of one triangular face of the pyramid.

Since the tent is in the form of a regular triangular pyramid, the area of one triangular face can be calculated using the formula:

Area of a triangle = (1/2) * base * height

In this case, the base is 6 ft and the slant height is 8 ft. Let's denote the height of the triangle as h.

Using the Pythagorean theorem, we can find the height (h) of the triangle:

8^2 = 6^2 + h^2
64 = 36 + h^2
h^2 = 28
h = √28 ft

Now, we can substitute the values of the base (6 ft) and the height (√28 ft) into the area formula to find the area of one triangular face:

Area of one triangular face = (1/2) * 6 * √28 = 3 * √28 ft^2 ≈ 16.7 ft^2

Since there are four triangular faces on the tent, the total surface area of the tent is 4 * 16.7 ft^2 = 66.8 ft^2

This is less than the given surface area of 100 ft^2, which indicates that the calculated height (√28 ft) is incorrect.

If Niko provides the correct surface area of the tent, I can help calculate the height of the base to the nearest tenth.