a stainless steel patio heater is a square pyramid. the length of one side of the base is 19.8 in The slant height of the pyramid is 92.4 What is the height of the pyramid? The height of the pyramid is about nothing in. (Round to one decimal place as needed.)
To find the height of the pyramid, we first need to identify the triangular faces of the square pyramid. Each triangular face forms a right-angled triangle with the slant height (hypotenuse) as the third side.
Since the base of the pyramid is a square, all sides are equal. Therefore, the length of each side of the base is 19.8 inches.
Now we can use the Pythagorean theorem to find the height of the pyramid. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides.
Let's represent the height of the pyramid as "h." We can then create the equation: h^2 + (1/2 * side length)^2 = slant height^2
Plugging in the values we know:
h^2 + (1/2 * 19.8)^2 = 92.4^2
Simplifying the equation:
h^2 + (9.9)^2 = 92.4^2
h^2 + 98.01 = 8532.96
h^2 = 8532.96 - 98.01
h^2 = 8434.95
To find the height, we need to take the square root of both sides of the equation:
h ≈ √8434.95
Using a calculator, we find that the approximate square root of 8434.95 is 91.8 (rounded to one decimal place).
Therefore, the height of the pyramid is approximately 91.8 inches.
Draw a side view, and it is clear that
h^2 + (19.8/2)^2 = 92.4^2