10.6.2 Formulas for Areas
If you know the formula for the area of a rectangle, you can work out formulas for the area of a parallelogram, shown below, and a triangle.
Take a parallelogram, cut off the left edge, and place it next to the right edge to make a rectangle. This has the same area as the parallelogram.
The area of the rectangle can be found by multiplying its base by its height.
Now if you cut this parallelogram in half along a diagonal, there are two possibilities:
In each case, the parallelogram has been split into two triangles that have the same area. So the area of each triangle is half the area of the parallelogram.
This gives a general formula for the area of a triangle:
The height goes through the vertex that is opposite the base and is always perpendicular to the base, as shown in the diagram above.
To find the area of a triangle quickly, you can work out half the base and multiply it by the height (or vice versa). Or you can multiply the base by the height and then divide by 2.
The diagram below is a rough sketch of the gable end of a house that needs weatherproofing.
To work out the quantity of materials required, the area of the wall is needed. We can break this problem down by splitting the area into a rectangle and a triangle, then working out these areas and finally adding the two areas together to get the total. Assume the measurements have been made to the nearest 10 cm.
The triangle has a base of length 8 m and a perpendicular height of 2 m. So, the area can be calculated as follows:
That means the total area of the gable end = .
Go to the next page to have a go at some examples for yourself.