The length of the rectangle is 6cm. what is its area if the perimeter is 18cm?

1) Find the width of the rectangle.

We know the perimeter of the rectangle and its length. Let’s write the formula for the perimeter of a rectangle:

P = (a + b) × 2,

where a is the length of the rectangle, b is the width.

Let us express the width, b from the formula:

P = 2a + 2b,

2b = P – 2a,

b = (P – 2a) ÷ 2.

b = (18 – 2 × 6) ÷ 2 = (18 -12) ÷ 2 = 6 ÷ 2 = 3 cm.

2) Find the area of the rectangle.

The area of a rectangle is equal to the product of the lengths of its sides.

Let’s write a formula for calculating the area of a rectangle:

S = a × b,

S = 6 × 3 = 18 cm²

Answer: the area of the rectangle is 18 cm².