Calculating the maximum capacity of an arena

Speaker 1: Gareth, we have a potential new band coming in next month.

They would like us to have a standard stage with a mixing desk slightly larger, as they've got a really cool light and sound experience.

We need to try and work out the full capacity so we can get back to the promoter of the show.

Speaker 2: Yeah, OK. No problem.

Speaker 1: Great. As you know, our standard stage is 18.2 metres times 12.8 metres and for this event, the mixer's going to have to be bigger.

It's 13.55 metres by 12.18 metres so it can fit in all the lighting and sound.

Don't forget with the standing concert, each person needs 0.38 metres squared gaps for our health and safety regulations.

Speaker 2: OK, no worries.

Speaker 1: Thank you.

Speaker: First, I need to work out the total space available after taking into account the desk and stage and with all the seating removed.

The mixing desk dimensions are 13.55 metres by 12.18 metres.

To work out the area in square metres, I multiply the width by the length.

13.55 by 12.18 equals 165.039 square metres.

I'm going to round to two decimal places, so that's 165.04 square metres.

Now the stage size. That's 18.2 times 12.8 which equals 232.96 square metres. OK, so I've worked out the area taken up by the stage and mixing desk.

I will add these two sizes together.

165.04 plus 232.96 equals 398 square metres.

The total space of the arena is 2,895 square metres.

So now I must subtract 398 square metres, the area taken up by the stage and mixing desk from 2,895 square metres.

So the total area I have left is 2,497 square metres.

Speaker 1: (TO AUDIENCE) The total space of the arena left is 2,497 square metres.

Now I need to work out how many people we can fit into this arena.

To do this I divide the remaining area with the space needed per person.

0.38 square metres when standing, so 2,497 divided by 0.38 equals 6,571 people to the nearest whole number.

Speaker 2: (TO OTHER PEOPLE) Hey Gareth how did you get on?

Speaker 1: Yeah, great thanks. I've just done the calculations for you.

I just worked out that we can have a maximum of 6,571 people for a standing show.

Speaker 2: That's great stuff shall we go and let the promoter know?

Speaker 1: Yeah, OK.