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Competencies covered

MSFGN2001: Make measurements and calculations


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If you think of length as being one dimensional, that is, going in one direction only, then area is two dimensional, because it has length and width.

Let's have a look at the area of some common shapes.

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Squares and rectangles

The area of any square or rectangle is simply its length times its width. For example, if a rectangle is 3 metres long and 2 metres wide, its area is:

      Length x width = 3 m x 2 m = 6 square metres (m²)

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What if you had a sheet of particleboard measuring 3.6 m x 1.8 m? Its area is simply:

      Length x width = 3.6 m x 1.8 m = 6.48 m²

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Let's say you cut the sheet of particleboard in half diagonally, forming two equal triangles. The area of each triangle is exactly half of the original rectangle. That is:

      Length x height ÷ 2 = 3.6 x 1.8 ÷ 2 = 3.24 m²

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This proves that a triangle is half the area of the rectangle or square that it came from.

So even if you had a triangle that didn't have a right angle in it, the calculation is still the same, because you could simply divide the triangle into 2 triangles, and the rectangle around it into 2 rectangles.

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But note that you must always measure the height of the triangle at right angles (90 degrees) to the base.

You can't measure the diagonal line in the triangle, because that's not the true height of the rectangle that goes around it.

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You may remember from your school days that the formula for the area of a circle is: Π r², where Π is 3.14, and 'r' is the radius of the circle.

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If you're happy using that formula you can stay with it, but you might prefer this simplified version - which is actually the same, but just put in different terms:

     Area of a circle = diameter x diameter x 3.14
                                  2             2

Another way of writing this is:

     Area = (diameter ÷ 2) x (diameter ÷ 2) x 3.14

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Here's an example. If a circle is 1.2 m in diameter, what's its area? The answer is shown below.

Area = (diameter ÷ 2) x (diameter ÷ 2) x 3.14

       =   (1.2 ÷ 2)       x       (1.2 ÷ 2)       x       3.14

       =   0.6       x       0.6       x       3.14

       =   1.13 m²

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So where does 3.14 come from? This is actually the approximate ratio between the circumference, or outside measurement, of the circle and its diameter.

In other words, the circumference of a circle is roughly 3.14 times longer than its diameter.

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Compound shapes

If you can break a shape up into its basic parts, you can calculate its area by adding the separate areas together.

Example 1: L shape

This L shape is basically two rectangles. What is its area? Note that the measurements in the diagram are shown in millimetres, so you'll need to convert them into metres for the calculation. A good way to set out the workings is as follows.

          Rectangle 1:   1.9 x 0.85 = 1.615 m²

          Rectangle 2:   0.95 x 0.85 = 0.808 m²

          Total area:   1.615 + 0.808 = 2.423 m²

Written mathematically, this would be:

          (1.9 x 0.85) + (0.95 x 0.85) = 2.423 m²

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Example 2: Gable end of a house

This shape is a triangle plus a rectangle. Again, you can set out your workings in the same way.

          Triangle: 1.59 x 4.125 ÷ 2 = 3.279 m²

          Rectangle: 2.75 x 4.125 = 17.05 m²

          Total area: 5.58 + 17.05 = 22.63 m²

Written mathematically: (1.8 x 6.2 ÷ 2) + (6.2 x 2.75) = 22.63 m²

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Example 3: Half circle around a bay window

This floor area is made up of a rectangle and a semicircle.

The formulas and calculations for finding this area are as follows:

        Semicircle area = area of circle ÷ 2.

In other words:

        Semicircle = (diameter ÷ 2) x (diameter ÷ 2) x 3.14 ÷ 2

                        = (3.3 ÷ 2) x (3.3 ÷ 2) x 3.14 ÷ 2

                        = 1.65 x 1.65 x 3.14 ÷ 2

                        = 4.274 m2

Now we can do the rest of the calculation:

      Rectangle: 6.0 x 3.3 = 19.8 m2

      Total area: 4.274 + 19.8 = 24.074 m2

Written mathematically: (3.3 ÷ 2 x 3.3 ÷ 2 x 3.14 ÷ 2) + (6.0 x 3.3) = 24.074 m2

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Learning activity

Audio 14 (mp3 |6|KB)

You have been asked to measure up the floor area of the house shown below.

What is the total area in square metres?

Enter your answer into the cell, and click on the 'Check your answer' button to see if you were right.

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