Integral to calculate surface area of a right triangular prism

Question

$$ \iint_{s}xyzdS $$ base is a triangle with vertices (1, 0, 0), (0, 1, 0) e (0, 0, 1) and the other base is in plan x + y + z = 4. How can I evaluate and see the figure?

Answer 1

HINT:

From the right triangle (PA,PC,BC) in the base plane point P appears pushed up to B by 1 unit (PB=GF=1) keeping AE,CD the same. The (CD,AE,BF) are parallel sides extruded by lengths 3 units.

Base triangle is not right angled. The extrusion sides (D,G,P,C) are parallelograms. None of the faces contains a right angle.

Answer 2

That's th prism I did, don't know if it is right tho https://i.stack.imgur.com/kEer5.png