A Triangular Pyramid Is Cut By A Plane. In Which Case Is The Cross Section A Quadrilateral?

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 .

You are watching: A triangular pyramid is cut by a plane. in which case is the cross section a quadrilateral?

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.”

Answer from: aubreyfoster

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 from: toya96

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

Step-by-step explanation:

When a plane intersects a plane, it forms a line.

A triangular pyramid has four faces.

To form four straight lines and therefore a quadrilateral, the intersecting plane must intersect all four faces.

Answer from: Jeiku3629

(D) is the right answer

Step-by-step 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.

Answer from: bronson62

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

Step-by-step explanation:

In order to get a quadrilateral, that is, a polygon with 4 sides, it is necessary that the plane intersect 4 faces of the 3d shape. A triangular pyramid has four faces, a base and three lateral faces. So, the plane have to intersect them all.

Answer from: laurentsupreme
For the answer to the question above, if you cut it directly to the middle, then the cross section will be an isosceles trapezoid, which is also a quadrilateral.I hope my answer helped you. Feel free to ask more questions. have nice day!
Answer from: villarrealc1987
When you cut it directly to the middle…then the cross section will be an isosceles trapezoid… Which is also a quadrilateral

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