We are asked to find the surface area of a triangular prism. To do that we must add the areas of each of the faces of the prism, that is, three rectangles and two triangles. The area of each rectangle is:
[tex]A_{\text{rectangles }}=5\operatorname{cm}\times12\operatorname{cm}+5\operatorname{cm}\times12\operatorname{cm}+5\operatorname{cm}\times12\operatorname{cm}[/tex]
Solving the operations we get:
[tex]A_{\text{rectangles}}=180cm^2[/tex]
Now we find the area of the triangles, knowing that the area of a triangle is the product of its base by its height over two, like this:
[tex]A_{\text{triangle}}=\frac{(base)(height)}{2}[/tex]
The base is 5 cm and the height is 6cm, replacing we get:
[tex]A_{\text{triangle}}=\frac{(5\operatorname{cm})(6\operatorname{cm})}{2}=15cm^2[/tex]
Now we add both areas having into account that there are two triangles, like this:
[tex]A=A_{\text{rectangle}}+2A_{\text{triangle}}[/tex]
Replacing we get:
[tex]\begin{gathered} A=180+2(15) \\ A=210 \end{gathered}[/tex]
therefore, the surface area is 210 square centimeters
