An illustration shows a square pyramid with labeled parts. The front and left faces of the pyramid and base are visible. The back and right faces are not visible. The back and right base edges are not visible but their position is indicated by a dashed line. The left base edge shows a length of 16 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and shows a height of 15. A right angle is indicated where the dotted height line meets the base.
Find the slant height of the square pyramid.
To find the slant height of the square pyramid, we can use the Pythagorean Theorem.
The slant height, the height, and half the length of the base form a right triangle. The height is 15 feet and half the length of the base is 8 feet (16 feet divided by 2). Let the slant height be represented by x.
By using the Pythagorean Theorem:
x^2 = 8^2 + 15^2
x^2 = 64 + 225
x^2 = 289
x = √289
x = 17
Therefore, the slant height of the square pyramid is 17 feet.