Question

a right triangular prism is sliced perpendicular to its base and parallel to the left face.
what is the shape of the cross section?
the cross section is a
parallelogram
rectangle
right triangle
trapezoid

Explanation:

Step1: Analyze the Prism and Slice

A right triangular prism has triangular bases and rectangular lateral faces. The slice is perpendicular to the base (which is a triangle) and parallel to the left face (a right triangle - shaped face? Wait, no, the left face of a right triangular prism (when base is a right triangle) is a rectangle? Wait, no, let's think again. A right triangular prism: the bases are right triangles, and the lateral faces are rectangles. When we slice perpendicular to the base (so along the direction of the height of the prism) and parallel to the left face (which is a rectangle? Wait, no, the left face of a right triangular prism (with right triangle base) would be a rectangle? Wait, no, the left face - if the base is a right triangle, the lateral faces are rectangles. Wait, the slice is parallel to the left face. The left face of the right triangular prism (since it's a right prism, the lateral edges are perpendicular to the base) - so the left face is a rectangle? Wait, no, the left face: the base is a right triangle, so the three lateral faces are rectangles. Wait, when we slice perpendicular to the base (so the slice is along the direction of the prism's length, perpendicular to the triangular base) and parallel to the left face (which is a rectangle? No, wait the left face - looking at the diagram, the left face is a right triangle? Wait the diagram shows a right triangular prism, so the left face (the face we are slicing parallel to) is a right triangle. Wait, no, the problem says "parallel to the left face". Let's visualize: a right triangular prism has two triangular bases (right triangles) and three rectangular lateral faces. Wait, maybe the left face is a triangular face? No, the bases are the triangular faces. Wait, the diagram: the prism has a triangular top and bottom (bases) and rectangular sides. The slice is perpendicular to the base (so vertical, if the base is horizontal) and parallel to the left face. The left face - in the diagram, the left face (the face on the left side of the prism) is a rectangle? No, the left face - looking at the 3D figure, the left face would be a triangle? Wait, no, the bases are the two triangles (front and back? Or top and bottom). Wait, the problem says "sliced perpendicular to its base and parallel to the left face". Let's recall: in a right triangular prism, the lateral edges are perpendicular to the bases. So the bases are triangles (right triangles), and the lateral faces are rectangles. So if we slice perpendicular to the base (so along the lateral edge direction) and parallel to the left face (which is a rectangular lateral face? No, the left face - maybe the left face is a triangular face? Wait, no, the two triangular faces are the bases. So the left face must be a rectangular lateral face? Wait, no, the diagram shows the prism with a triangular top and bottom (bases) and rectangular sides. The slice is a plane that is perpendicular to the base (so it's a vertical plane, if the base is horizontal) and parallel to the left face. The left face - in the diagram, the left face (the face we are slicing parallel to) is a right triangle. Wait, the slice is parallel to the left face, which is a right triangle. So when we slice the prism perpendicular to the base (so the slice is a plane that cuts through the prism, perpendicular to the triangular base) and parallel to the left face (a right triangle), then the cross - section should be a right triangle. Wait, let's check the options: parallelogram, rectangle, right triangle, trapezoid. Since we are slicing parallel to the left face (which is a right triangle) and perpendicular to the base (so the slice will have the same shape as the left face, which is a right triangle). So the cross - section is a right triangle.

Step2: Eliminate Other Options

- Parallelogram: A parallelogram has opposite sides parallel, but our slice should be a triangle, so eliminate.
- Rectangle: A rectangle has four right angles, but our slice is parallel to a triangular face, so it should be a triangle, eliminate.
- Trapezoid: A trapezoid has four sides with one pair of parallel sides, but our slice is a triangle, eliminate.
- Right triangle: Since we are slicing parallel to the left face (a right triangle) and perpendicular to the base (so the slice will have the same shape as the left face, a right triangle), this is correct.

Answer:

right triangle