equilateral, isosceles, and scalene.
You would cut off a corner.
A square
Make a cut that goes diagonally across three adjoining faces of the cube. If a side of the cube is 's'. Each side of the triangle will square_root(2)*s.
Infinitely many.
equilateral, isosceles, and scalene.
You would cut off a corner.
No, a cube cannot have an octagonal cross-section.
It is a triangle.
It depends on the angle of the plane of the cross section. If it is parallel to the cube's face (or equivalently, two adjacent edges) the cross section will be a square congruent to the face. If the plane is parallel to just one edge (and so angled to a face), the cross section will be a rectangle which will have a constant width. Its length will increase, remain at a maximum level and then decrease. If neither, it will be a hexagon-triangle-hexagon-triangle-hexagon (triangles when passing through a vertex).
A cube and an equilateral triangle based pyramid
A square, a cube, a diamond, a equilateral triangle, a triangular based pyramid made of equilateral triangles...
A square.
A square
Make a cut that goes diagonally across three adjoining faces of the cube. If a side of the cube is 's'. Each side of the triangle will square_root(2)*s.
The cross sectional area of a triangular prism is simply the area of the base. The formula for the area of a triangle in one half base times height. Remember that a triangular prism by definition has a triangle for a base.
Equilateral, Isosceles or Scalene. For the latter two they could be acute or right angled