Answer
$15 \sqrt {26}$
Work Step by Step
The surface Area of the part $z=f(x,y)$ can be computed as: $A(S)=\iint_{D} \sqrt {1+(f_x)^2+(f_y)^2} dx \ dy$
and, $\iint_{D} dA$ is the projection of the surface on the xy-plane.
The area of the given surface is as follows: $A(S)=\iint_{D} \sqrt {1+(3)^2+(4)^2} dA=\sqrt {26} \iint_{D} dA$
and, $\iint_{D} dA$ is the area of the region inside $D$.
Area of the rectangle $=(5-0) \times (4-1) =15$
Then, we have: $A(S)=\sqrt {26} \iint_{D} dA \\ A(S) =15 \sqrt {26}$
