Question

A triangular pyramid is cut by a plane. In which case is the cross section a quadrilateral?

Answer 1

Answer:

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

Step-by-step 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

Step-by-step 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."