## 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}

## 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}