Solve problems involving perimeter and area of triangles, rectangles, squares, parallelograms, kites, trapeziums and the combinations of these shapes.

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

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