Given data:
The given triangular pyramid.
The expression for the slant height is,
[tex]\begin{gathered} L=\sqrt[]{(10)^2-(\frac{12}{2}})^2 \\ =8 \end{gathered}[/tex]The surface area of the triangular pyramid is,
[tex]\begin{gathered} SA=\frac{\sqrt[]{3}}{4}(12)^2+\frac{1}{2}(12+12+12)8 \\ =36\sqrt[]{3}+144 \end{gathered}[/tex]Thus, the surface area of the triangular pyramid is 144+36(3)^(1/3).
