Question

slices were made parallel to and perpendicular to the base of a 3 - dimensional shape. the resulting cross - sections are shown. choose all the shapes that could result in these cross - sections. cone cube triangular prism rectangular prism triangular pyramid rectangular pyramid

Explanation:

Step1: Analyze cross - sections of cone

A cone's parallel cross - section is a circle and perpendicular is a triangle or an isosceles triangle - not a rectangle, so not cone.

Step2: Analyze cross - sections of cube

A cube's parallel and perpendicular cross - sections are squares or rectangles, but not an equilateral triangle, so not cube.

Step3: Analyze cross - sections of triangular prism

A triangular prism can have a rectangle as a cross - section parallel to the base and a triangle as a cross - section perpendicular to the base, so it is a triangular prism.

Step4: Analyze cross - sections of rectangular prism

A rectangular prism's cross - sections are rectangles or squares, not an equilateral triangle, so not rectangular prism.

Step5: Analyze cross - sections of triangular pyramid

A triangular pyramid's parallel cross - section is a similar triangle and perpendicular cross - section is a triangle, but getting a non - degenerate rectangle is not possible in the described way, so not triangular pyramid.

Step6: Analyze cross - sections of rectangular pyramid

A rectangular pyramid's cross - sections are triangles or trapezoids or other polygons, not a simple rectangle and an equilateral triangle in the described way, so not rectangular pyramid.

Answer:

triangular prism