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Application of Number

Level 2

Area of Complex Shapes - Tutorial 4

This example is a little harder since we are not given the lengths of all of the sides.

Below is the plan of a plot of land ready for building on. We want to find the area of it. The measurements are in m.

First we need to split it into rectangles. Below is one way.

We now have three rectangles A, B and C. We can work out the area of each by multiplying the length by the width in each case.

For rectangle C, this is easy.

For rectangle B it is slightly different. We can see that the width is 100m. To get the length we need to add together 120m and another 120m from the top.

This means that the area of B is

240 x 100 = 24000 m²

For rectangle A we know the length (120), but we don't know the width. What we do know is that the right side of the shape is 200 long. This means that the total length of the left side must add up to 200 also. So far we know that rectangle C uses 20 and rectangle B uses 100. So the width of rectangle A must make the left side add up to 200.

20 + 100 + width of A  = 200
20 + 100 +       80        = 200

So the width of A is 80 and the length is 120. Now we can work out the areas.

Now that we know the areas of each of the rectangles we can add them together.

A    +      B    +    C    =    Area of Land

9600 + 24000 + 3600   = 37200 m²

Now test yourself by doing the following assessment. Try to get at least 80% correct. Try this test again in a few days time to make sure that you have remembered how to do it.

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