What is the smallest and largest perimeter of a polygon with an area of 20?

The polygon with the smallest perimeter is the megagon

The polygon with the largest perimeter is the triangle

Step-by-step explanation:

An equilateral triangle with area = 20 has

0.5 * a²*sin60 = 20

a = 6.796

Hence, perimeter = 20.39

A square of area 20 has perimeter = 4*√20 = 17.9

A regular pentagon of area = 20 has perimeter = 3.41 * 5 = 17.05

Hence as the number of sides is increasing, the ratio of the Area to the Perimeter also increases

Therefore, a triangle has the largest perimeter with an area of 20 while a megagon with a million sides has the smallest perimeter with an area of 20.