Question

When is a rectangle a regular polygon?

Answer 1

Hint: Here in this question, we have to explain or check whether the rectangular is a regular polygon. For this, first we need to consider the one rectangle then the properties of regular polygon. if the conditions or properties are satisfied by rectangle then it’s called a regular polygon otherwise it’s not a regular polygon.

Complete step-by-step answer:
The regular polygon is the flat, closed, straight-sided shape and must also have another property. i.e., Every interior and exterior angle in the regular polygon is equal to every other interior and exterior angle, and every side is equal in length to every other side.
In geometry, Rectangle is a four sided-polygon, having all the internal angles equal to $${90}^{\circ }$$ degrees. The two sides at each corner or vertex meet at right angles. The opposite or parallel sides of the rectangle are equal in length which makes it different from a square.
The shape of rectangle represented as:

By the properties of the rectangle:
Only Parallel or opposite sides are equal but a regular polygon must be all sides are the same or equal length.
Hence, Rectangle can never be a regular polygon.

Note: Remember, a regular polygon should be both equilateral (all sides are the same length) and equiangular (all internal angles of the same measure). Rectangle is only an equiangular but not an equilateral. If the rectangle satisfies both equiangular and equilateral then the shape will be a square.