Calculate the Area: Four x-cm Squares at y-cm Square Vertices

We will refer to two separate areas: the area of the square with side y and the total area of the four squares with sides x,

We'll use the formula for the area of a square with side b:

$S=b^2$and therefore when applying it to the problem, we get that the area of the square with side y in the drawing is:

$S_1=y^2$Next, we'll calculate the area of the square with side x in the drawing:

$S_2=x^2$and to get the total area of the four squares in the drawing, we'll multiply this area by 4:

$4S_2=4x^2$Therefore, the area of the required figure in the problem, which includes the area of the square with side y and the area of the four squares with side x is:

$S_1+4S_2=y^2+4x^2$Therefore, the correct answer is A.