Relationship between Perimeter and Area

10.3

Relationship between Perimeter and Area

The relationship between the perimeter and the area of a rectangle:

(i) Rectangles with the same perimeter

The area will decrease if the difference between the length and the width increase.
The area will be the largest when the rectangle is a square.

(ii) Rectangles with the same area

The perimeter will increase if the difference between the length and the width decrease.
The perimeter will be the smallest when the rectangle is a square.

Solve a problem:

Example

Given the perimeter of the square floor of a hall is \(82\text{ m}\).

Calculate the area of the floor of the hall.

Noted that the length of each side of a square are equal.

So, the length of each side is

\(82\text{ m}\div4=20.5\text{ m}\).

Thus, the area of the floor of the hall is

\(\begin{aligned} &\space\text{Area} \\\\&=20.5\times20.5 \\\\&=420.25\text{ m}^2 .\end{aligned}\)