The surface are correspond to the the areas of the faces and base of the net.
The faces are four triangles, two with a height of 4.5 in and base of 6 in., and two with a height of 5 in. and base of 4 in.
The base of the net has sides of length 4 and 6 in.
We can add all this surfaces to find the total surface area:
[tex]\begin{gathered} A=A_b+2\cdot A_{t1}+2\cdot A_{t2} \\ A=(4\cdot6)+2\cdot(\frac{6\cdot4.5}{2})+2\cdot(\frac{4\cdot5}{2}) \\ A=24+27+20 \\ A=71 \end{gathered}[/tex]
Answer: the surface area is 71 in^2.
