Year 7 Interactive Maths - Second Edition

Calculating the Area

Area of a Square

The area of a square that has a side-length of 1 cm is 1 square centimetre (or 1 cm²).  To find the area of a square by the method of counting squares, we divide the square into smaller squares of one centimetre side-length .

Consider a square that has a side-length of 4 cm.

Using the method of counting squares, we find that the area of the square is 16 cm².

Clearly, the square contains 4 rows of 4 squares.  Therefore:

This suggests that:

The area of a square is equal to its side-length multiplied by its side-length.  That is:

Using the pronumerals A for area and s for side-length, we can write it simply as:

This is the formula for the area of a square.

Example 1

Find the area of a square flower-bed of side 15 m.

Solution:

Note:

To find the area of a region enclosed within a plane figure, draw a diagram and write an appropriate formula.  Then substitute the given values and use a calculator, if necessary, to obtain the required area.