Final answer:
To find the perimeter of the given land, calculate the distance between each pair of consecutive vertices and add them up.
Step-by-step explanation:
To find the perimeter of the land with vertices A (1,1), B (3,1), C (1,6), and D (3,6), we need to calculate the distance between each pair of consecutive vertices and then add them up.
Using the distance formula, we find that the distance between A and B is √((3 - 1)^2 + (1 - 1)^2) = √2 units. The distance between B and C is √((1 - 3)^2 + (6 - 1)^2) = √26 units. The distance between C and D is √((3 - 1)^2 + (6 - 6)^2) = √4 units. Lastly, the distance between D and A is √((1 - 1)^2 + (1 - 6)^2) = √25 units.
Adding up these distances, we get √2 + √26 + √4 + √25 = √2 + 5√2 + 2 + 5 = 6 + 6√2 units.