Question

select the correct answer.
a triangular pyramid is cut by a plane. in which case is the cross section a quadrilateral?

a. when the plane is perpendicular to the base and passes through the apex

b. when the plane is parallel to the base of the pyramid

c. when the plane intersects the base and two lateral faces of the pyramid

d. when the plane intersects the base and all three lateral faces of the pyramid

Explanation:

• Option A: A plane perpendicular to the base and through the apex will cut a triangular cross - section (a triangle), as it passes through three edges (from apex to base vertices), so the cross - section is a triangle.
• Option B: A plane parallel to the base of a triangular pyramid will create a cross - section that is similar to the base, which is a triangle.
• Option C: If the plane intersects the base and two lateral faces, the number of intersection edges is 3 (1 from the base and 2 from the lateral faces), so the cross - section is a triangle.
• Option D: When the plane intersects the base (1 edge) and all three lateral faces (3 edges), the total number of intersection edges is 4. A four - sided figure is a quadrilateral, so the cross - section will be a quadrilateral.

Answer:

D. when the plane intersects the base and all three lateral faces of the pyramid