10x10 square

Each horizontal lines will have 10 matchsticks.

You will have 11 horizontal lines

Therefore you will have 10*11 horizontal matchsticks

Same work with the vertical matchsticks

You will have 11 vertical lines of 10 matchsticks.

therefore you will have 11*10=110 vertical matchsticks.

In total you will have 220=2*11*10

If you have a 20x20 square.

Again you will have 21 horizontal lines of 20 matchsticks and 21 vertical lines of 20 matchsticks. Therefore you have 20*21*2 matchsticks in total.

Now for a nxn square

we have horizontal n+1 horizontal lines of n matchsticks and n+1 vertical lines of n matchsticks. In total we have n*(n+1)*2 matchsticks.

**Therefore the formula is 2n(n+1) matchsticks for a n x n square.**

It is matches the result for n=10, n=20 and of course n=1 n=2, n=3.

**Formula:** 2n(n+1)

matchsticks

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now