Q: What does a plane that cuts a triangular pyramid parallel to its base result to?

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It creates a trapezium frustum.

Suppose the top face of the pyramid is ABCD with the square EFGH directly below it.Suppose AC and BD meet at P, the apex of the pyramid.Make a cut with a plane through P which is parallel to AB and goes through EF.Make a cut with a plane through P which is parallel to BC and goes through FG.Make a cut with a plane through P which is parallel to CD and goes through GH.Make a cut with a plane through P which is parallel to DA and goes through HE.The result will be the square-based pyramid PEFGH.

A pyramid is a generic term and can have any number (>3) of plane faces. A triangular pyramid has 4 faces, a rectangular one has 5, and so on. A pyramid whose base has n sides has n+1 faces.

It depends on the pyramid. If it is a square based pyramid, a horizontal plane will give a square cross section, a plane inclined by a rotation parallel to one of the base axes will give a rectangular cross section whereas a plane inclined by rotation along both basal axes will result in a parallelogram cross section. Not sure how you get a parallelogram from a pentagonal or hexagonal (etc) pyramid.

Yes. Four solid angles comprising 12 plane angles.

Related questions

A triangular pyramid has 5 planes. * * * * * In fact, a triangular pyramid is also known as a tetrahedron and as its name suggests, it has 4 plane faces.

It creates a trapezium frustum.

Triangular

Suppose the top face of the pyramid is ABCD with the square EFGH directly below it.Suppose AC and BD meet at P, the apex of the pyramid.Make a cut with a plane through P which is parallel to AB and goes through EF.Make a cut with a plane through P which is parallel to BC and goes through FG.Make a cut with a plane through P which is parallel to CD and goes through GH.Make a cut with a plane through P which is parallel to DA and goes through HE.The result will be the square-based pyramid PEFGH.

All cross sections of a square pyramid that are parallel to the base are squares

A pyramid is a generic term and can have any number (>3) of plane faces. A triangular pyramid has 4 faces, a rectangular one has 5, and so on. A pyramid whose base has n sides has n+1 faces.

It depends on the pyramid. If it is a square based pyramid, a horizontal plane will give a square cross section, a plane inclined by a rotation parallel to one of the base axes will give a rectangular cross section whereas a plane inclined by rotation along both basal axes will result in a parallelogram cross section. Not sure how you get a parallelogram from a pentagonal or hexagonal (etc) pyramid.

Yes. Four solid angles comprising 12 plane angles.

The answer depends mainly on the plane which is used to divide the prism.The result can be a rectangular prism (or a cube), a trapezoidal prism, a triangular prism, but to get really exotic shapes the cutting plane needs to be not parallel to any of the faces or diagonals of the prism.

A 3-dimensional shape. 5 plane faces: 3 rectangular, 2 triangular. Triangular faces parallel to one another. 6 vertices 9 edges

It could have just one - a plane (not plan!) parallel to its bases and halfway between them.

This is an impossible shape. The only 3-d shape with 4 plane faces is a tetrahedron (triangular pyramid). While its base is a triangle, all of its other faces are also triangles and so cannot have parallel sides.