Given the composite figure shown in the exercise, you can identify that it is formed by a rectangular prism and a triangular prism.
The surface area of a rectangular prism can be calculated by using this formula:
Where "l" is the length, "w" is the width and "h" is the height.
In this case, you can identify that:
![\begin{gathered} l=8\operatorname{cm} \\ w=6\operatorname{cm} \\ h=7\operatorname{cm} \end{gathered}]()
Then, substituting values into the formula and evaluating, you get:
![\begin{gathered} SA_(rp)=2wl+2hl+2hw \\ SA_(rp)=(2\cdot6\operatorname{cm}\cdot8\operatorname{cm})+(2\cdot7\operatorname{cm}\cdot8\operatorname{cm})+(2\cdot7\operatorname{cm}\cdot6\operatorname{cm}) \\ SA_(rp)=292\operatorname{cm} \end{gathered}]()
The surface area of a triangular prism can be found by using this formula:
Where "b" is the base of the base, "h" is the height of the base, "P" is the perimeter of the base, and "H" is the height of the triangular prism.
In this case:
![\begin{gathered} b=6\operatorname{cm} \\ h=7\operatorname{cm} \\ P=6\operatorname{cm}+7\operatorname{cm}+9\operatorname{cm}=22\operatorname{cm} \\ H=6\operatorname{cm} \end{gathered}]()
Then, substituting values and evaluating, you get:
![\begin{gathered} SA_(tp)=(6\operatorname{cm})(7\operatorname{cm})+(22\operatorname{cm})(6\operatorname{cm}) \\ SA_(tp)=174\operatorname{cm} \end{gathered}]()
Therefore, the surface area of the composite figure can be found by adding the surface area of the rectangular prism and the surface area of the triangular prism:
![\begin{gathered} SA=292\operatorname{cm}+174\operatorname{cm} \\ SA=466\operatorname{cm}^2 \end{gathered}]()
Hence, the answer is:
![SA=466\operatorname{cm}^2]()