Answer:
2np + p²
Step-by-step explanation:
The general formula for the area of a square is A = s², where s = the length of one side of the square. In the case of the smaller square the area would be: n x n = n². Since the side of the larger square is 'p' inches longer, the length of one side is 'n + p'. To find the area of the larger square, we have to take the length x length or (n +p)².
Using FOIL (forward, outside, inside, last):
(n + p)(n+p) = n² + 2np + p²
Since the area of the first triangle is n², we can subtract this amount from the area of the larger square to find out how many square inches greater the larger square area is.
n² + 2np + p² - n² = 2np + p²
