I am struggling with this can someone please explain to me how this works or if I'm doing it right

Part A is correct. Nice work

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Part B is close, but you forgot about some of the '1's that you'll need to add up. Check out the diagram below. I've added blue x's and 1's to show the various side lengths. You should have 6 copies of 1 to add up leading to +6 at the end, not +2. The perimeter is 2x+2y+6

Side note: the terms inside the boxes/rectangles represent the area of each little piece. For instance the upper left rectangle is 1 by x so its area is 1*x = x square units.

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For part C, refer to the diagram below. The perimeter is y+1+y+1+1+y+1+y = 4y+4

Or you can think of each side having (y+1) and we have four of those sides leading to 4(y+1) = 4y+4 as the perimeter.

The area is y^2+y+y+1 = y^2+2y+1. This can be found by using the FOIL rule on (y+1)^2