A square with an area of 16m² has a side of 4m and a perimeter of 16m. So it cannot have a perimeter of 20m (it would need a side length of 5m, an area of 25m²).
Note that, although the area and perimeter look the same because of the number 16, the units of area are square measurements, but the units of perimeter are linear (cm, inches, metres, etc.).
In general, the perimeter and area do not have the same number, so you can draw a square with an area and perimeter that are numerically different. For example, a square of side 5cm has an area of 25 sq cm and a perimeter of 20cm; a square of side 3cm has an area 9 sq cm and perimeter 12cm.