click on all the shapes that can be created by cutting a rectangular pyramid perpendicular to its base. a. pentagon b. rectangle c. square d. trapezoid e. triangle

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# Brief Explanations:
1. **Understanding the Pyramid and Cross - Section**: A rectangular pyramid has a rectangular base. When we cut it perpendicular to its base:
   - If we cut through the apex (the top point) and perpendicular to the base, the cross - section will be a triangle. Because the sides of the pyramid are triangular faces, and a cut through the apex and perpendicular to the base will intersect the triangular faces, resulting in a triangular cross - section.
   - If the base of the rectangular pyramid is a square (a special case of a rectangle), and we make a cut parallel to the base (but the question says perpendicular to the base, wait, no, if we cut perpendicular to the base but not through the apex? Wait, no, the standard cross - section when cutting a rectangular pyramid perpendicular to its base:
     - The base is a rectangle (or square). If we cut the rectangular pyramid perpendicular to its base, the cross - section's shape depends on the cut. If we cut through the apex and perpendicular to the base, the cross - section is a triangle. If the base is a square, and we make a cut perpendicular to the base (but maybe not through the apex? Wait, no, the problem says "cutting a rectangular pyramid perpendicular to its base". Let's recall the properties:
       - A rectangular pyramid has a rectangular base and triangular lateral faces. When we cut it perpendicular to the base (i.e., the cut is vertical if the base is horizontal), if we cut through the apex, the cross - section is a triangle (since we are cutting through the triangular faces). If the base is a square (a type of rectangle), and we make a cut perpendicular to the base (but maybe parallel to one of the sides of the base? Wait, no, perpendicular to the base means the cut is at a right angle to the base.
       - Let's analyze each option:
         - **Option A: Pentagon**: A pentagon has 5 sides. A rectangular pyramid has a rectangular base (4 sides) and triangular faces. A cut perpendicular to the base cannot result in a pentagon because the maximum number of sides from a cut perpendicular to the base would be related to the number of sides of the base and the triangular faces. A rectangular pyramid has 4 - sided base and triangular faces, so a perpendicular cut will not create a pentagon.
         - **Option B: Rectangle**: If we cut the rectangular pyramid perpendicular to the base but parallel to one of the sides of the base (not through the apex), we can get a rectangle. Wait, no, actually, the base is a rectangle. If we make a cut perpendicular to the base (i.e., along a plane that is vertical if the base is horizontal) and parallel to one of the pairs of opposite sides of the base, the cross - section will be a rectangle. Also, a square is a special case of a rectangle.
         - **Option C: Square**: If the base of the rectangular pyramid is a square (a square is a type of rectangle), and we make a cut perpendicular to the base (parallel to the sides of the square base), the cross - section can be a square. Since a square is a special case of a rectangle, and the base can be a square, this is possible.
         - **Option D: Trapezoid**: A trapezoid has only one pair of parallel sides. When we cut a rectangular pyramid perpendicular to the base, the cross - section will have either two pairs of parallel sides (like a rectangle or square) or three sides (a triangle). So a trapezoid cannot be formed by a perpendicular cut to the base of a rectangular pyramid.
         - **Option E: Triangle**: When we cut the rectangular pyramid perpendicular to the base and through the apex, the cross - section will be a triangle. Because the cut will pass through the apex and two opposite edges of the base, forming a triangle.
2. **Conclusion on Valid Shapes**:
   - Triangle (E): As explained, cutting through the apex perpendicular to the base gives a triangle.
   - Rectangle (B): Cutting perpendicular to the base (parallel to the sides of the rectangular base) gives a rectangle.
   - Square (C): If the base is a square, cutting perpendicular to the base (parallel to the sides of the square base) gives a square.
   - Pentagon (A) and Trapezoid (D) are not possible.

# Answer:
B. rectangle, C. square, E. triangle

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