Question

the cross section of a solid figure sliced perpendicular to its base is shown.

decide whether or not the cross section could have come from each of the figures listed below.

triangular prism \t\tyes \t\tno
cylinder \t\t\tyes \t\tno
square pyramid \t\tyes \t\tno
rectangular prism \t\tyes \t\tno
cone \t\t\t\tyes \t\tno

Explanation:

Step1: Analyze Triangular Prism

A triangular prism, when sliced perpendicular to its base (which is a triangle), can have a trapezoidal cross - section if the slice is not parallel to the lateral faces. So for triangular prism, the answer is Yes.

Step2: Analyze Cylinder

A cylinder, when sliced perpendicular to its circular base, will have a rectangular (or square) cross - section, not a trapezoid. So for cylinder, the answer is No.

Step3: Analyze Square Pyramid

A square pyramid, when sliced perpendicular to its square base (but not through the apex and not parallel to the base), can have a trapezoidal cross - section. So for square pyramid, the answer is Yes.

Step4: Analyze Rectangular Prism

A rectangular prism, when sliced perpendicular to its rectangular base (and not parallel to the faces), can have a trapezoidal cross - section. So for rectangular prism, the answer is Yes.

Step5: Analyze Cone

A cone, when sliced perpendicular to its circular base, will have a triangular cross - section (if through the apex) or a circular segment - like shape, not a trapezoid. So for cone, the answer is No.

Answer:

• triangular prism: Yes
• cylinder: No
• square pyramid: Yes
• rectangular prism: Yes
• cone: No