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Q: Why does the horizontal cross section of a pyramid form the shape of a square?

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The horizontal cross section of a rectangular pyramid is a rectangle.

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.

A 2D representation of a square-based pyramid is called a square pyramid net or a square pyramid template.

The following are some shapes having a square cross section: a cube, a cuboid, a square pyramid.

Depending on the inclination of the plane used for the cross-section, it could be a square, rectangle, trapezium, triangle.

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a square

a square

The horizontal cross section of a rectangular pyramid is a rectangle.

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.

A 2D representation of a square-based pyramid is called a square pyramid net or a square pyramid template.

The following are some shapes having a square cross section: a cube, a cuboid, a square pyramid.

It can be a square, a trapezium, a quadrilateral or a triangle - depending on the inclination of the plane which defines the cross section.

Depending on the inclination of the plane used for the cross-section, it could be a square, rectangle, trapezium, triangle.

square pyramid

I assume you mean between prism and pyramid. I suggest you look at some picture of prisms and pyramids, to get it perfectly clear. In any case, a prism has the same horizontal cross section from the bottom the top. On the other hand, the lines of a pyramid get together towards the top, to a point. If you take a horizontal cross section, at the base it will be larger, but the closer you get to the top, the smaller such a cross section will be.

cone, cylinder, rectangular prism, square pyramid and triangular prism

The cross section of a pyramid shrinks from the shape of the base down to a point as you move along its axis from the base to the apex. The cross section of a prism is constant along its axis.