The surface area of the square pyramid consists of the area of four identical triangles and the square base. The formulas to obtain the area of each one of those two kinds of figures are
[tex]\begin{gathered} A_{\text{square}}=l^2 \\ A_{\text{triangle}}=\frac{1}{2}bh \end{gathered}[/tex]
In our case,
[tex]l=b=6,h=9[/tex]
Thus, the surface area is
[tex]\begin{gathered} A_{\text{surface}}=A_{\text{square}}+4A_{\text{triangle}} \\ \Rightarrow A_{\text{surface}}=6^2+4(\frac{1}{2}6\cdot9)=36+2\cdot54=36+108=144 \\ \Rightarrow A_{\text{surface}}=144 \end{gathered}[/tex]
Thus, the answer is 144m^2
