A rectangular plot of lawn shown in the figure has dimensions x and y and is surrounded by a gravel pathway of width 2 m. What is the total area of the pathway ?

The pathway adds 2 m on every side, so the overall outer rectangle has length x+4 and width y+4 (2 m added on both left and right, top and bottom). The area of the region including the pathway is (x+4)(y+4); subtracting the lawn area xy gives the pathway area = (x+4)(y+4) − xy, which expands to 4x + 4y + 16. This algebraic simplification follows directly from expanding the product and cancelling xy terms, yielding the pathway area as 4x + 4y + 16. Therefore option 4 is correct.