Surface area

Solving for the length of the diagonal

$x = \sqrt{8^2 + 5^2} = \sqrt{89}$

Method 1.

Compute the surface area of $1$ cut then multiply it by $2$ .

$A = 3(5) + 3(8) + 3\sqrt{89} + 2(\frac{1}{2})(5)(8) = 107.3$

$2A = 2(107.3) =$ $\boxed{214.6m^2}$

Method 2.

Compute the area of the rectangular parallelepiped then add twice the area of the cutting plane.

$A = 2(3)(5) + 2(5)(8) + 2(3)(8) + 2(3)(\sqrt{89}) =$ $\boxed{214.6m^2}$