Question 242992
The best way to do this is to draw a diagram and mark in dashed lines the corner sections and centre section.

The whole area of the cardboard is equal to 154 inches^2. The corner sections are equal to 4x^2. The mid sections are equal to 2x(14-2x) and 2x(11-2x).

So we know that the total area of the cardboard minus the 4 corners minus the 4 mid sections must equal the centre bottom area of 80 inches^2.

{{{154-4x^2-2x(14-2x)-2x(11-2x) = 80}}}
{{{154-4x^2-(28x-4x^2)-(22x-4x^2) = 80}}}

{{{4x^2-50x+74 = 0}}} Rearrange to equal zero.

Use the quadratic formula to find x.

*[invoke quadratic "x", 4, -50, 74]

x cannot be 10.784 as this would mean it was longer than the sides which of course does not make sense! So it must be 1.7154 inches. So the size of the squares cut was 1.7154^2 = 2.942 inches^2.