In that case, you don't have enough information.
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only solids have "lateral area". triangles have "area". the area of a scalene triangle is given by heron's formula. height not needed.
You need to know the area of that cross-section. Once you have that number, the volume of the box is the product of (cross-section area) x (height).
A = 1/2bh then you use Pythagoras theorem to find the length of the other 2 sides, using the known value for the height and 1/2 of the bases value.
Volume = (height)(area base)
If you are only given the side lengths of a scalene triangle, it is impossible for you to find for the area, unless you are given more information... like the height of the triangle for example. If this is a right triangle you would like to find the area of, you can multiply the length of each leg with each other, and then divide that product by 2 to conclude the area of the triangle.