To find the height of the base, we first need to calculate the area of each triangular face of the pyramid. Since the tent is in the form of a regular triangular pyramid, each face is an equilateral triangle.
The total surface area of the tent is 100 ft^2, and there are four faces on the pyramid. Therefore, each face has an area of 25 ft^2.
The formula for the area of an equilateral triangle is A = (s^2 * sqrt(3))/4, where s is the side length of the triangle. Since the tent is in the form of a regular triangular pyramid, the base of the triangle is also the base of the pyramid.
We are given that the base of the tent is 6 ft, so the side length of each triangular face is 6 ft. Substituting into the formula:
25 = (6^2 * sqrt(3))/4
25 = (36 * sqrt(3))/4
100 = 36 * sqrt(3)
100/36 = sqrt(3)
2.78 = sqrt(3)
Now, we need to find the height of the base of the pyramid. We know that the slant height is 8 ft, and the height forms a right angle with the base, so we can use the Pythagorean theorem to find the height.
h = sqrt(8^2 - 3^2)
h = sqrt(64 - 9)
h = sqrt(55)
h = 7.4 ft
Therefore, the height of the base is approximately 7.4 ft.
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 answer