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

Step-by-step explanation:

A triangle pyramid is reduced by a plane, then the cross ar will it is in a quadrilateral when the intersecting aircraft forms a closed 4 sided polygon .You are watching: A triangular pyramid is cut by a plane. in which case is the cross section a quadrilateral?

We recognize that a triangular pyramid has 4 faces. For this reason to produce a quadrilateral, the intersecting plane must intersect all 4 faces.

From every the given options only in choice D the airplane will intersects all the 4 faces developing a closed polygon of 4 lines such that the cross section will it is in a quadrilateral.

hence, the ideal answer is " once the airplane intersects the base and also all three lateral deals with of the pyramid, the cross ar of the triangle pyramid will be a quadrilateral."

Answer from: aubreyfoster

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

Step-by-step explanation:

A quadrilater number has 4 sides and also it will certainly be developed only if the aircraft cuts every four faces of the pyramid. The only situation in i m sorry this happens is in option D (the base and also all three lateral faces of the pyramid), the intersection of 2 planes is a line, if the aircraft intercepts the pyramid in 4 areas the resulting figure is a four-sided polygon

Answer from: toya96

as soon as the plane intersects the base and also all 3 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 crossing all four faces.

Answer from: Jeiku3629

(D) is the best answer

Step-by-step explanation:

The cross section will it is in a quadrilateral when the intersecting airplane forms a closed four sided polygon in addition to the pyramid.

A triangular pyramid has 4 faces. So, to form four straight lines and therefore a quadrilateral, the intersecting aircraft must intersect all four faces.

A. In this instance the airplane will only intersect one next of the pyramid so four sided polygon can"t it is in formed.

B. That will only intersect the two sides of the pyramid yet the cross section will no be a quadrilateral.

C. In this instance the airplane will intersect 3 sides the the pyramid so the cross section will be a triangle not a quadrilateral.

D. In this situation the aircraft intersects all the four faces forming a closeup of the door polygon that 4 right lines therefore the cross section will it is in a quadrilateral.

So, the Correct option is (D) : once the airplane intersects the base and also all 3 lateral encounters of the pyramid, the cross section of the triangular pyramid will be a quadrilateral.

Answer from: bronson62

when the plane intersects the base and also all three lateral encounters of the pyramid

Step-by-step explanation:

In order to gain a quadrilateral, the is, a polygon through 4 sides, that is vital that the aircraft intersect 4 encounters of the 3d shape. A triangle pyramid has 4 faces, a base and three lateral faces. So, the aircraft have to crossing them all.

Answer from: laurentsupreme

For the answer come the question above, if you cut it straight to the middle, climate the cross section will it is in an isosceles trapezoid, i beg your pardon is likewise a quadrilateral.I hope my answer helped you. Feel free to ask more questions. Have nice day!

Answer from: villarrealc1987

When you cut it straight to the middle...then the cross section will be an isosceles trapezoid... I beg your pardon is also a quadrilateral

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