Apply the Pythagorean theorem to determine the height of the square pyramid h round to the answer to the nearest tenth

To apply the Pythagorean theorem to find the height of a square pyramid, we need the lengths of the base and slant height.

Let's assume that the base of the pyramid is a square with side length x, and the slant height is y.

According to the Pythagorean theorem, the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides (base side length and height). In this case, we have:

y^2 = x^2 + h^2

To solve for h (the height), we rearrange the equation as follows:

h^2 = y^2 - x^2

Next, we substitute the given values and solve for h.

Let's say the slant height, y, is 10 units and the base side length, x, is 6 units. Plugging these values into the equation, we get:

h^2 = 10^2 - 6^2
h^2 = 100 - 36
h^2 = 64

To find the height, we take the square root of both sides:

h = √64
h = 8 units

Therefore, the height of the square pyramid is 8 units when rounded to the nearest tenth.