A square pyramid is a three-dimensional solid shape with a square base and four triangular sides that meet at a common point (the apex). The slant height of a square pyramid is a line that runs from the apex to the midpoint of one of the sides of the square base. It is slanted, hence the name "slant height."
The slant height of a square pyramid can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of
the two shorter sides is equal to the square of the length of the hypotenuse. In this case, the slant height can be considered as the hypotenuse and the height of the triangular face can be considered as one of the shorter sides.
The formula to find the slant height x of a square pyramid can be expressed as:
x = √(h^2 + (side length / 2)^2)
Where h is the height of the pyramid and the side length is the length of one side of the square base.
For example, if the height of the pyramid is 8 units and the side length of the square base is 6 units, the slant height would be:
x = √(8^2 + (6 / 2)^2) = √(64 + 9) = √73 units
In conclusion, the slant height of a square pyramid can be found by using the Pythagorean theorem to find the length of the hypotenuse in a right triangle formed by the height of the pyramid and half the length of one side of the square base. The resulting value represents the slant height of the square pyramid.
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