Jason B. answered • 04/20/17

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The surface area of the pyramid is the area of the square plus the area of each of the triangle faces. The area of a square is length squared. We know the length is 5, so the area A

_{square}= 5^{2}= 25.The area of a triangle is 1/2 base times height. In this case, the base is 5 and the height is the slant height, h (to visualize this, look at a picture of pyramid slant height). The equation is: A

_{triangle}= 1/2 (5) (h) = 2.5h.There are four triangles, so the total surface area is A

_{surface}= A_{square}+ 4 (A_{triangle}) = 25 + 4 (2.5h) = 25 + 10h. We know the surface area is 175, so:25 + 10h = 175

10h = 150

h = 15

The slant height is 15 inches.