Answer:
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.
