Answer: Area = 4w² + 30w + 36
Step-by-step explanation:
Let w represent the width of the rectangular patio.
The rectangle patio has a length four times its width. It means that the length of the patio is 4w.
The formula for determining the area of a rectangle is expressed as
Area = length × width
If the boarder is 3 ft, the combined length of the patio and the boarder would be (4w + 3 + 3) = (4w + 6) feet
Also, the combined width of the patio and the boarder would be
(w + 3 + 3) = (w + 6) feet
Therefore, the expression for the area of the patio and boarder is
Area = (4w + 6)(w + 6)
Area = 4w² + 24w + 6w + 36
Area = 4w² + 30w + 36
