How to Determine the Area of Compound Rectangles

One of the most troublesome things you have to do with areas is find the total area of a shape made up of several rectangles. This may seem tricky, but after you see what’s going on, things start to make sense.

The trick is to split up the shape into smaller rectangles for which you either know or can figure out the length of each side. This is a little bit more of an art than a science – but as with everything else in maths and life, the more you practise, the easier the method gets.

Take the following steps if you need to find the area of a shape that isn’t a rectangle but is full of right angles:

1. Try to find somewhere to draw a line that splits the shape into two, smaller rectangles.

   If not, draw a line that splits off one rectangle and try to split the rest of the shape up into smaller rectangles. How many rectangles you have doesn’t matter – but you’re less likely to make mistakes if you use as few shapes as possible.

2. Work out the sides of each rectangle you have left over.

   You may need to do a bit of lateral thinking, but normally you just need to take something away from the total length of a side.

3. Find the area of each rectangle by multiplying the sides together.

   Write the answer in the middle of the rectangle so you don’t forget it.

4. Add up all of the areas you just worked out.

   The answer is your total area.

   

The figure starts with a wibbly shape and neatly cuts it into two rectangles with a sideways line near the top. Work out the height of the bigger rectangle, which is the only side you didn’t know to start with. Find the areas of the two rectangles and add up these two areas to get a final answer.

On the right, the rectangle is split up in a different way, giving three separate shapes. Again, work out the lengths of the sides, find the areas and add the areas to get a final answer. You end up with the same answer using both methods.