DESCRIBING CROSS SECTIONS RIGHT RECTANGULAR PRISM

An intersection is a point or set of points common to two or more geometric figures. A plane is a flat surface that extends forever in all directions.

A cross section is the intersection of a three-dimensional figure and a plane. Imagine a plane slicing through the pyramid shown, or through a cone or a prism.

The figure given below shows the intersection of a cone and a plane. The cross section is a circle.

The figure given below shows the intersection of a triangular prism and a plane. The cross section is a triangle.

A three-dimensional figure can have several different cross sections depending on the position and the direction of the slice.

For example, if the intersection of the plane and cone were vertical, the cross section would form a triangle.

More Examples

Example 1 :

The cross section of the above right rectangular prism is triangle.

Example 2 :

The cross section of the above right rectangular prism is rectangle.

Example 3 :

The cross section of the above right rectangular prism is parallelogram. 

Example 4 :

The cross section of the above right rectangular prism is rectangle. 

Example 5 :

The cross section of the above right rectangular prism is triangle or equilateral triangle.

Example 6 :

The cross section of the above right rectangular prism is rectangle. 

Example 7 :

The cross section of the above right rectangular prism is triangle. 

Example 8 :

The cross section of the above right rectangular prism is rainbow-shaped curve. 

Reflect

(In a right pyramid, the point where the triangular sides meet is centered over the base.)

What are the shape of the base and each side of the pyramid ?

The shape of the base is a rectangle and the shape of each side is a triangle.

Is it possible to have a circular cross section in a right rectangular prism ?

No, there are no curves in a right rectangular prism.

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