A rectangular pyramid is sliced perpendicular to the base. Choose all the shapes that could represent a cross-section resulting from the slice
1. Rectangle
2. Square
3. Triangle
4. Trapezoid
5. Pentagon
To determine the possible shapes resulting from slicing a rectangular pyramid perpendicular to the base, we need to consider the properties of cross-sections.
A cross-section is the shape that appears when we cut through an object. In this case, we are slicing the rectangular pyramid.
When slicing a rectangular pyramid perpendicular to the base, the cross-sections can have various shapes. Let's consider each possibility:
1. Triangle: If the slicing plane intersects three edges of the rectangular pyramid, forming a triangle, then a triangular cross-section is obtained.
2. Rectangle: If the slicing plane intersects two opposite edges of the rectangular pyramid, then a rectangle cross-section is obtained.
3. Trapezoid: If the slicing plane intersects only one edge of the rectangular pyramid, resulting in a quadrilateral with one pair of parallel sides, then a trapezoid cross-section is obtained.
Hence, the possible shapes representing a cross-section resulting from slicing a rectangular pyramid perpendicular to the base are a triangle, a rectangle, and a trapezoid.
The possible shapes that could represent a cross-section resulting from the slice of a rectangular pyramid perpendicular to the base are:
1. Triangle: If the slice is horizontal, it would cut through the apex of the pyramid, resulting in a triangle.
2. Rectangle: If the slice is parallel to one of the rectangular faces of the pyramid, it would result in a rectangle.
These are the two possible shapes that could represent a cross-section resulting from the described slice.