ANSWER
[tex]864\text{ cm}^2[/tex]
EXPLANATION
To find the surface area of the triangular pyramid given, apply the formula:
[tex]A=\text{ Base Area}+\frac{1}{2}(\text{ Perimeter }*\text{ Slant Height})[/tex]
First, we have to find the slant height of the pyramid by applying Pythagoras theorem:
[tex]l^2=12^2+(\frac{18}{2})^2[/tex]
where l represents the slant height.
Solve for l in the equation above:
[tex]\begin{gathered} l^2=144+81=225 \\ \\ l=\sqrt{225} \\ \\ l=15\text{ cm} \end{gathered}[/tex]
Now, find the surface area of the pyramid:
[tex]\begin{gathered} A=(18*18)+\frac{1}{2}((4*18)*15) \\ \\ A=324+\frac{1}{2}(72*15) \\ \\ A=324+540 \\ \\ A=864\text{ cm}^2 \end{gathered}[/tex]
That is the answer.
