An oblique cut on a cuboid

The sides of the triangle are the diagonals of the faces of the cuboid.

They are from Pythagorean theorem $\sqrt{7^2+5^2}=\sqrt{74}, \sqrt{7^2+4^2}=\sqrt{65}, \sqrt{4^2+5^2}=\sqrt{41}$

Heron's formula will give us the area of the triangle based on its sides.

The semi-perimeter $s$ is the sum of the sides divided by two $s\approx11.533$

$A=\sqrt{s(s-\sqrt{74})(s-\sqrt{65})(s-\sqrt{41})}=\boxed{24.54}$

Here is a general parametric solution with help from Mathematica(TM) software: Assume u, v, and w are the sides of the triangle EFG. We first start with Heron's formula, and then inserts u, v, and w with Pythagorean theorem from a, b, and c. Mathematica will simplify the expression, and then we insert the numbers.