Nico has an outdoor play tent in the form of a rectangular triangular pyramid covered in fabric on all four sides the surface area of the tent is 100 ft and 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 rectangular triangular pyramid can be calculated using the formula:
Surface Area = base area + 2 * (0.5 * base * slant height)
Given that the surface area is 100 ft, the base is 6 ft, and the slant height is 8 ft, we can substitute these values into the formula:
100 = (0.5 * 6 * slant height) + 2 * (0.5 * 6 * 8)
Simplifying the equation:
100 = 3 * slant height + 2 * 24
100 = 3 * slant height + 48
Subtracting 48 from both sides:
3 * slant height = 52
Dividing both sides by 3:
slant height = 52 / 3 ≈ 17.3
To calculate the height of the base, we will use the Pythagorean theorem. In a right triangle, one side is the height, the other side is the slant height, and the hypotenuse is the height of the tent. We can use the equation:
(hypotenuse)^2 = (height)^2 + (slant height)^2
Let's call the height of the tent "h."
h^2 = (height)^2 + (17.3)^2
Since the base is rectangular, the height of the tent is also the height of the base, so we're looking for "h."
h^2 = h^2 + (17.3)^2
Subtracting h^2 from both sides:
0 = (17.3)^2
This equation has no solution. Therefore, the given dimensions for the tent are not possible.