The pyramid shown has a square base that is 18 inches on each side. it has a surface area of 864 square inches. what is the slant height?

The first step is to find the relationship between the square base and the surface area.

Surface area (SA) = area of the square (SS) + area of triangles.4(AT) 

Thus we can conclude area of triangles 4(AT) = SA - SS = 864 - (18*18)

4(AT) = 864 - 324 = 540

Each triangle = 540/4 = 135 square in.

An area of one triangle (AT)= (base* slant height)/2

The base = 18 in.

slant height = 2(AT)/base = 2(135)/18 = 15

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