Yes it can.
equilateral, isosceles, and scalene.
You would cut off a corner.
No, a cross section of a cube cannot be a pentagon. The cross section of a cube is formed by slicing through the cube, and the maximum number of sides that can be produced in such a slice is four, resulting in a quadrilateral. Any cross section of a three-dimensional shape like a cube will have sides that align with the edges of the cube, which cannot create a five-sided polygon like a pentagon.
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-section of a cube can vary depending on how it is cut. If sliced parallel to one of its faces, the cross-section will be a square. If cut diagonally, the cross-section can be a rectangle or a more complex polygon, depending on the angle and position of the cut.
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...
No, a cross section of a cube cannot be a pentagon. The cross section of a cube is formed by slicing through the cube, and the maximum number of sides that can be produced in such a slice is four, resulting in a quadrilateral. Any cross section of a three-dimensional shape like a cube will have sides that align with the edges of the cube, which cannot create a five-sided polygon like a pentagon.
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-section of a cube can vary depending on how it is cut. If sliced parallel to one of its faces, the cross-section will be a square. If cut diagonally, the cross-section can be a rectangle or a more complex polygon, depending on the angle and position of the cut.
A square.
A square