Apply the Pythagorean Theorem to determine the height of the square pyramid, h, round to the nearest tenth

Answer 1

To find the height of the square pyramid, we can apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the height of the pyramid, h, is the hypotenuse of a right triangle with the base length being half of the side length of the square base. Let's represent the side length of the square base as s.

Using the Pythagorean Theorem, we get:

h^2 = (s/2)^2 + s^2
h^2 = s^2/4 + s^2
h^2 = 5s^2/4

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

h = sqrt(5s^2/4) = s*sqrt(5)/2

Since we know the side length of the square base, we can substitute that value into the formula to determine the height. Let's say the side length of the square base is 6 units:

h = 6*sqrt(5)/2
h = 6.7 units

Therefore, the height of the square pyramid is approximately 6.7 units when the side length of the square base is 6 units. This height is rounded to the nearest tenth.