Given that the perimeter P is 4m and the length is 1/3 of the width, we can set up an equation to find the area.

Let the width be W and the length be L.

From the information given:
P = 2(L + W) = 4m
L = W/3

Substitute L = W/3 into the perimeter equation:
2(W/3 + W) = 4
2W/3 + 2W = 4
2W + 6W = 12
8W = 12
W = 1.5m

Now we can find the length:
L = W/3 = 1.5/3 = 0.5m

The area of the rectangle (S) is given by:
S = L x W = 0.5m x 1.5m = 0.75 square meters

Therefore, the area of the rectangle is 0.75 square meters.