math grid

When counting the red squares we can't count the corners twice.

Here are 3 ways of figuring it out, which all get the same answer and can be used with any sized grid thats even.(eg, 20x20 or others)

Method 1 of solving it is by doing 10 x 4 - 4 or 10 + 10 + 10 + 10 - 4. We are subtracting four because those are the corners that would have already been counted, as well.

This makes 36 and works with other grids if they are even.
Proof:
10 x 4 = 40
40 - 4 = 36

If we were using letters and not numbers:

4n - 4 = (the answer)

or

n + n + n + n - 4 = (the answer)

We can do 10 + 10 + 8 + 8, is adding the two rows and the two sides together.

its 8 because the corners have been counted.

it adds up to 36.
The Proof:
10 + 10 = 20 and 8 + 8 = 16
20 + 16 = 36.

If we letters it would be:

2n + 2n-2 = (the answer)

or

n + n + n-2 + n-2 = ( the answer). 

My way.  if it has 4 sides (the purple) 10 on each - 4 (the red) = 36