Question

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

Answer 1

D

Explanation:

a quadrilateral has 4 sides, so you need it to intersect 4 sides of the pyramid, option D is the only option that intersects 4 sides

Answer 2

(D) is the right answer

Explanation:

The cross section will be a quadrilateral when the intersecting plane forms a closed four sided polygon along with the pyramid.

A triangular pyramid has four faces. So, to form four straight lines and therefore a quadrilateral, the intersecting plane must intersect all four faces.

A. In this case the plane will only intersect one side of the pyramid so four sided polygon can't be formed.

B. It will only intersect the two sides of the pyramid but the cross section will not be a quadrilateral.

C. In this case the plane will intersect three sides of the pyramid so the cross section will be a triangle not a quadrilateral.

D. In this case the plane intersects all the four faces forming a closed polygon of 4 straight lines so the cross section will be a quadrilateral.

So, the Correct Option is (D) : When the plane intersects the base and all three lateral faces of the pyramid, the cross section of the triangular pyramid will be a quadrilateral.