Question

the pyramid shown has a square base that is 6 feet on each side. it has a surface area of 84 square feet. what is the slant height?

Answer 1

Surface area of a pyramid = $lw+l \sqrt{ \frac{w^2}{2}+h^2 } +w \sqrt{ \frac{ l^{2} }{2} + h^{2} }$
$84=6 \times 6 + 6( \sqrt{ \frac{6^2}{2} +h^2}) +6( \sqrt{ \frac{6^2}{2} +h^2}) \\ 84=36+12( \sqrt{ \frac{36}{2} +h^2}) \\ 48=12( \sqrt{ 18 +h^2}) \\ 4= \sqrt{18 +h^2} \\ 16=18 +h^2 \\ h^2=16-18=-2 \\ h= \sqrt{-2}$
Which is not real. Hence, the question is not correct.