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Slant height is the height of the triangular face of the pyramid. Here since the square base has dimensions 12 by 12, the base length of this triangle is 12 inches. Join the midpoints of one side of the square base to the opposite side of the square base. This midsegment you created also has a length of 12inches. Since the height of the pyramid is 10 inches and connects from the vertex of the pyramid to the midpoint of this midsegment, we see we have a triangle that is 10 inches high and base is 12 inches. Inside it is a right triangle with base 6 inches and height 10 inches. Let us use Pythagorean Theorem to find the hypotenuse.
This hypotenuse = Slant Height.
6^2 + 10^2 = (slant height)^2
or in other symbols: 6*6 + 10*10 = (slant height)*(slant height)
36 + 100 = 136
slant height = square root of 136 = 11.661 inches
Answer choice A. 11.66
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