Question

the question is on the sheet .The shaded region is the area within the figure but not the corner squares

Answer 1

Based on the information given in the exercise, you know that the shaded region has this area:

$6x^2-2xy+3y^2$

And the area of each square region in the corners is:

$4x^2$

Since there are four square regions, you can multiply that the area of any of them by 4, in order to find the total area of them:

$4(4x^2)=16x^2$

Then, in order to find the total area of the figure, you must add the area of the shaded region and the total area of the square regions:

$(6x^2-2xy+3y^2)+(16x^2)=22x^2^{}-2xy+3y^2$

Therefore, the total of the figure is:

$22x^2-2xy+3y^2$