Question

what is the area of a triangular prism of 18 top across base, 10 high, one protrusion is 10.34 and the other protrusion is 13.4

Answer 1

Trying to picture the shape and meaning of “protusion”.
The measure of 18 I take to mean the perpendicular from the vertex of the triangular base to its opposite side, which would be the height of the top and bottom triangles.
The protusions I take to mean the measure from the perpendicular where it meets the base to the left end and right end of the base.
The area you want I take to be the total surface area of the top and bottom triangles plus the areas of the three rectangular sides.
First the triangular ends: area=2*(1/2*base*triangle height)=(10.34+13.4)*18=23.74*18=427.32.
We need the lengths of the three sides of the triangle to get the dimensions of the rectangular sides of the prism.
Base length=23.74. To get the other two sides we use Pythagoras:
sqrt(10.34^2+18^2)=20.7585 and sqrt(13.4^2+18^2)=22.4401.
The total rectangular surface area is 10(23.74+20.7585+22.4401)=669.39, added to the triangular areas is 1096.71.