# Right pyramid

If a right pyramid has a base of quadrilateral, must the base be either a rectangle or a square but not other possibility?

It seems to me that rhombus, parallelogram, trapezium and kite are all impossible, since their diagonals are not equal...

Thank you.

I am quite sure that the base can be a rectangle also!

I just wonder if it can be other possibilities...

Rhombus, parallelogram, trapezium and kite?

### 2 個解答

• 7 年前
最愛解答

The definition of 'right' is regular, 'right pyramid' is a pyramid whose base is a regular polygon. And, in which the segment connecting its vertex to the center of its base is perpendicular to the plane of the base.

So, if a right pyramid has a base of quadrilateral, as the base is a regular polygon, so it must be a square, no other case.

2014-03-19 10:17:04 補充：

In Maths world, 'Right pyramid' is defined as a pyramid for which the apex lies directly above the centroid of the base.

As rectangle, rhombus, parallelogram, those centroid are all directly under the apex, so these can be called 'a right pyramid'.

For kite and trapezium, they are not.