Walter wants to fence an area 400 m2 . What is the least amount of fencing he will require?

Answer 1

sqr400= 20

4x20 = 80 meters of fencing required

smallest perimeter is a square for a rectangle

but smaller yet is a circular enclosure (or any regular polygon with more than 4 sides, the more sides the less fencing required. As the sides approach infinity, the polygon approaches a circle)

area = 400 = pi(r)^2

r^2 = 400/pi

r = 20/sqrpi

circumference = the perimeter for a circle = 2pi(r) = 2pi(20/sqrpi) = 40sqrpi = about 40(1.77245)= 70.9 meters which is less than a square enclosure perimeter.