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Year 7 Interactive Maths - Second Edition


Calculating the Area

Often, we use a formula to calculate the area of plane figures such as squares, rectangles, triangles or circles.


Area of a Square

1 square centimetre

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.

4 rows of 4 squares

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:

Area equals 16 square centimetres


This suggests that:

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

Area equals length squared


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

Area equals s squared

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:
Area is 225 square metres Square of side-length 15 m

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.


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