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

Explanation:

A quadrilater figure has 4 sides and it will be formed only if the plane cuts all four faces of the pyramid. The only case in which this happens is in option D (the base and all three lateral faces of the pyramid), the intersection of two planes is a line, if the plane intercepts the pyramid in 4 places the resulting figure is a four-sided polygon

Answer 2

Answer: D) when the plane intersects the base and all three lateral faces of the pyramid

Explanation:

• A triangular pyramid is cut by a plane, then the cross section will be a quadrilateral when the intersecting plane forms a closed four sided polygon .

We know that a triangular pyramid has four faces. Thus to create a quadrilateral, the intersecting plane must intersect all four faces.

From all the given options only in option D the plane will intersects all the four faces producing a closed polygon of four lines such that the cross section will be a quadrilateral.

hence, the right answer is " 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."