What is the relationship between perimeter and area?

Answer 1

Perimeter is the distance AROUND any particular object where area is the amount of space inside the object (2dimentional).

Let's say you have a yard 10 feet long, by 11 feet wide.

The perimeter is the distance AROUND your yard or 10+10+11+11 = 42ft

The AREA is the amount of space inside or L*W or 10*11 = 110ft^2

Suppose I change the dimensions of the yard without changing its perimeter (42 ft) and see what happens to the area. Suppose the length and width are 20ft and 1 ft respectively. The perimeter is still 20+1+20+1=42. The area however is 20X1 =20 ft2 Now if we take the yard to be a square one of 10.5 ft side then the perimeter still remains 42 ft. but the area becomes 110.25 ft2. Now suppose I assume that the perimeter of a circle is 42 ft. What will the area of such a circle be? Now we know that the circumference of a circle is 2x3.14(pi)Xr = 42 ft. Therefore r = 6.687 ft. r2= 44.715 ft2 therefore area of the circle is 4xpixr2= 561.63 ft 2. Thus we can deduce that given a known perimeter a circular shape has or occupies the largest area. What happens if the shape is irregular? Say a irregular polygon? Would my deduction that the cicrular shape has the largest area remain valid?