Content description

Apply the enlargement transformation to familiar two-dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115)

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

Enlarging squares

If we start with a square, we can enlarge it by drawing a second square with side lengths two, three, ten or more times larger.

Here is a square with one-centimetre sides.

Perimeter = 4 cmArea = 1 cm²

Here is a square with two-centimetre sides. What do you notice about the perimeter and area of the larger square?

Perimeter = 8 cmArea = 4 cm²
A square with sides two times that of the original square has twice its perimeter.
A square with sides two times that of the original square has four times its area.

If we enlarge the 1 cm square and make the sides 3 cm, we get a square like this.

The side length of the square is 3 cm, so the perimeter is 12 cm and its area is 9 cm².
A square with side lengths three times that of the original has nine times its area.