To calculate the area of the tile pattern needed, first calculate the area of the pentagon and the area of the square, then add them together.
The area of the pentagon can be divided into a rectangle (base of the pentagon with length 6 and height of 3) and a triangle (with base of 3 and height of 3).
Area of rectangle = base x height = 6 x 3 = 18
Area of triangle = 0.5 x base x height = 0.5 x 3 x 3 = 4.5
So, area of the pentagon = Area of rectangle + Area of triangle = 18 + 4.5 = 22.5 square units
The area of the square is simply side x side = 3 x 3 = 9 square units.
Therefore, the total tile needed for the pattern is 22.5 + 9 = 31.5 square units.