Question

an architect designs a building by starting with a solid figure and slicing through it. the cross section is shown in light blue. what solid figure did the architect start with? the design is based on a dropdown menu with options: rectangular prism, triangular prism, triangular pyramid, square pyramid

Explanation:

Step1: Analyze the solid figure's cross - section and shape

The given solid figure, after slicing, has a rectangular - like cross - section and the overall shape is consistent with a rectangular prism. A rectangular prism has six rectangular faces (in general, some faces can be squares too). When we slice a rectangular prism, we can get cross - sections that are rectangles (or other polygons depending on the slice, but in this case, the initial solid is a rectangular prism). A triangular prism has triangular bases, a triangular pyramid (tetrahedron) has a triangular base and three triangular faces, and a square pyramid has a square base and four triangular faces. The given figure's shape is more in line with a rectangular prism.

Step2: Eliminate other options

• Triangular prism: It has triangular bases, but the given figure does not have triangular bases as part of its main structure before slicing.
• Triangular pyramid: It has a triangular base and three triangular lateral faces, which is not the case here.
• Square pyramid: It has a square base and four triangular lateral faces, which is not the shape of the given figure.

Answer:

The design is based on a rectangular prism.