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
rectangular prism
triangular prism
triangular pyramid
square pyramid

Explanation:

Step1: Analyze the cross - section and the solid

The given solid has a cross - section (the light blue part) and the overall shape. A triangular prism has two triangular bases and three rectangular faces. When we slice a triangular prism, we can get a cross - section that is consistent with the given figure. A rectangular prism has six rectangular faces, and slicing it would not give a shape that matches the given solid's structure. A triangular pyramid (tetrahedron) has a triangular base and three triangular faces, and a square pyramid has a square base and four triangular faces. Their cross - sections and overall shapes are different from the given figure.

Step2: Identify the solid

By comparing the properties of the given solid (from the cross - section and the visible parts) with the properties of the options:

• Rectangular prism: Incorrect, as its faces and cross - sections are not consistent with the given figure.
• Triangular prism: Correct, because a triangular prism has triangular bases and rectangular lateral faces, and the slicing shown is consistent with a triangular prism's structure.
• Triangular pyramid: Incorrect, as its shape is more like a pyramid with a triangular base and sloping faces, not matching the given figure.
• Square pyramid: Incorrect, as it has a square base and triangular lateral faces, not matching the given figure.

Answer:

The design is based on a triangular prism.