Use the image to answer the question Find the slant height of the square pyramid.
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Apologies, but as an AI text-based model, I am unable to view or analyze images. However, I can provide you with the steps to find the slant height of a square pyramid using the given measurements.
To find the slant height of a square pyramid, you need to know the length of the pyramid's slant height and the height of the pyramid.
If you are given the length of the slant height and the height of the pyramid, you can simply use the Pythagorean theorem to find the slant height. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In the case of a square pyramid, the height of the pyramid is one of the legs of the right triangle, and the slant height is the hypotenuse. The slant height is also the distance from the apex of the pyramid to the midpoint of one of the sides.
If you are given the length of one side of the square base, you can use the Pythagorean theorem to find the slant height, as follows:
1. Divide the length of one side of the square base by 2 to find the length of the adjacent side of the right triangle.
2. Use the Pythagorean theorem: slant height squared = height squared + adjacent side squared.
3. Take the square root of both sides to find the slant height.
For example, if you are given the length of one side of the square base as 12 units and the height of the pyramid as 10 units, you can find the slant height using the steps above:
1. The length of the adjacent side of the right triangle is 12 / 2 = 6 units.
2. Apply the Pythagorean theorem: slant height squared = 10 squared + 6 squared.
slant height squared = 100 + 36 = 136.
3. Take the square root of both sides to find the slant height: slant height = √136 ≈ 11.66 units.
Therefore, the slant height of the square pyramid is approximately 11.66 units.