What is the perimeter of 16 square centimeters?

Answer 1

There are an infinite number of shapes with an area of 16 square centimetres. The one with the smallest perimeter is a circle of radius 2.2568 cm (to 4 dp). Such a circle will have a perimeter of 14.1796 cm.

This value for the perimeter can be increased by changing the circle into an ellipse: making the ellipse flatter and longer (increasing its eccentricity) so that the perimeter increases without changing the area. There is no upper bound to the perimeter.

This can also be done for quadrilaterals, with the smallest one being a 4cm x 4cm square. But you could have a rectangle with sides 0.4 cm and 40 cm and a perimeter of 80.8

or 0.04 cm and 400 cm and a perimeter of 800.08 cm

or 0.004 cm and 4000 cm and a perimeter of 8000.008 cm

and so on - without limit.

Or you could have triangles, or polygons with 5 or more sides.

The important point is that area does not determine the perimeter.