The rectangle has twice the length of the square side.
The square has a side of 2 yards.
Then, we have to calculate the area of the square and the rectangle and add them.
The area of the square is equal to the square of its side (2 yards):
[tex]A_s=l^2=2^2=4\text{ sq yd}[/tex]The rectangle area is equal to the product of the length (equal to the side length, 2 yd) and the width (2 times the side of the square, 4 yd):
[tex]A_r=l\cdot w=2\cdot4=8\text{ sq yd}[/tex]If we add them, we get the total surface of the carpet:
[tex]A=A_s+A_r=4+8=12\text{ sq yd}[/tex]Answer: the carpet is 12 square yards [Option A].
