Working out how much paint is needed to decorate a room using bar modelling

Speaker: So I've just moved into this flat with a few of my friends and we're just about to start decorating.

I'm an apprentice painter/decorator, so obviously I've been landed the job of sorting out the painting.

At school, maths was not my favourite subject.

I just didn't think it would be very important to me.

But since starting this new job, I soon realised how much maths I actually needed.

At first I was a bit unsure when I was told to work out an area and then to work out how many pots of paint I needed for the area, but I had this really good maths tutor at college that told me about bar modelling.

And then when I saw it in a visual sort of way, it just made so much more sense to me.

So bar modelling is dead simple. You don't need to be able to draw or anything like that - it's just using rectangles to represent a problem visually, and then when I saw it like that, it just clicked.

(PHONE RINGS) That'll be my friend now.

She's just gone to the shops to pick up some paint so we can get started on the decorating.

'I've found the paint we picked.

Tin says coverage of 13m² per litre.

Tins are 1 litre, 2.5 litres or 5 litres.'

OK, so I need to work out the total area of the walls I'm going to paint and then I can work out how many pots of paint I actually need.

Let's go have a look at this room.

Speaker: So I need to work out how much paint we need to decorate this room.

So to do that, I need to work out the total area of the walls that I'm going to be painting.

Right, so I know that the opposite walls are going to be the same size, but there's a window here and a door there, which obviously don't need painting, so I need to remember to take that away from the total area.

To make more sense of this, let me just draw a diagram of the room.

Right, let's see what the measurements are.

Let's start off with this wall, as it's a bit more straightforward.

To find the area we need to multiply the length by the height.

So this one is 3.1 multiplied by 2.3, which gives me a total of 7.13 metres squared.

And then for the other wall, 2.3 multiplied by 2.7, which gives me 6.21 metres squared.

And then to find the total I just need to add them together, which is 13.34 metres squared.

So the other two walls are the same height and the same length but I need to take away the door and the window from the total area.

So this top bar is the total area and then at the bottom I need to add the door and the window, which means this remaining bit will be the area of the wall that needs to be painted.

So the area of the door is 1 by 2, which is 2 metres squared, and then the area of the window… 1.8 metres squared.

So I need to subtract that from the total area which is 13.34 minus 1.8, minus 2, 9.54.

Actually, no, because I need include the other two walls that I worked out before…

…gives me 22.88 metres squared and that is the total area of the walls that I need to paint.

Speaker: So if the total area is 22.88, and I'll probably want to do two coats of it just to be safe, that is 45.76 metres squared.

I'm gonna round up to 46 metres squared, so it'll be easier to calculate how many tins of paint I actually need.

So if I know that 1 litre covers 13 metres squared and I have an overall area of 46 metres squared, so that'll be in my top bar.

I then need to draw out each litre below to see how many 13s go into 46.

Right, so I can see the best way for me to do this is to divide.

3.538, which is just over 3 and a half litres, but let me just double-check it.

45.5, and I need it to cover 45.76.

It's a bit more… I mean I guess I could make the 3.5 litre work, but then I wouldn't have any room for touch-ups.

So maybe I'm best off just getting the 4.5, or if it's cheaper, just the 5-litre one.

Right, well, I think I've earned a tea!