We are given the following formula for the surface area of a prism:
[tex]A=2f+2t+2r[/tex]
"f" is the area of the front face, in this case, the front face is a rectangle, the area of a rectangle is given by the product of its base and its height. For the front face rectangle, its base is 8cm and its height is 4 cm, therefore, "f" is equal to:
[tex]f=(8\operatorname{cm})(4\operatorname{cm})=32\text{ cm}^2[/tex]
Now, for "t", the area of the top face, is also a rectangle with a base of 8 cm and a height of 3 cm, therefore its area is:
[tex]t=(8\operatorname{cm})(3\operatorname{cm})=24\text{ cm}^2[/tex]
For "r", we have a base of 3cm and a height of 4cm, therefore, the area is:
[tex]r=(3\operatorname{cm})(4\operatorname{cm})=12\text{ cm}^2[/tex]
Replacing in the formula for the area of the prism, we get:
[tex]\begin{gathered} A=2f+2t+2r \\ A=2(32\text{ cm}^2)+2(24\text{ cm}^2)+2(12\text{ cm}^2) \end{gathered}[/tex]
Solving the operations in the parenthesis, we get:
[tex]A=64+48+24[/tex]
Solving the sum
[tex]A=136\text{ cm}^2[/tex]
