The height of the segment from the apex of the pyramid to the base is 10 feet. The length of the diagonal of the square base is 4 feet.

Calculate the volume

volume = (1/3) base x height

for the base: let the side be x ft
x^2 + x^2 = 16
x=√8 or 2√2

Vol = (1/3) (√8)^2 (10) = 80/3 cubic feet

To calculate the volume of a pyramid, you need to know the base area and the height.

In this case, we are given the height of the segment from the apex of the pyramid to the base, which is 10 feet. However, we need to find the base area first before calculating the volume.

Given that the length of the diagonal of the square base is 4 feet, we can find the length of each side of the square base by dividing the diagonal length by the square root of 2, which is approximately 1.414.

So, each side of the square base is 4 / 1.414 ≈ 2.828 feet.

Now, we can calculate the base area by squaring the length of one side of the square base. Hence, the base area is (2.828)^2 ≈ 8.

Finally, we can calculate the volume of the pyramid by multiplying the base area by the height and dividing the result by 3.

Therefore, the volume of the pyramid is (8 * 10) / 3 = 80 / 3 ≈ 26.67 cubic feet.