## Area

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.

### 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

### 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

### 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 m^{2}

Now we can do the rest of the calculation:

Rectangle: 6.0 x 3.3 = 19.8 m^{2}

Total area: 4.274 + 19.8 = 24.074 m^{2}

Written mathematically: (3.3 ÷ 2 x 3.3 ÷ 2 x 3.14 ÷ 2) + (6.0 x 3.3) = 24.074 m^{2}

### 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.

21.59 | m² |