Calculate the area of the rectangle.

The rectangle has a length of $6 \text{ mm}$ and a width (height) of $4 \text{ mm}$.
The formula for the area of a rectangle is $A_{rectangle} = \text{length} \times \text{width}$.

$$A_{rectangle} = 6 \text{ mm} \times 4 \text{ mm} = 24 \text{ mm}^2$$

The base of the triangle is the same as the length of the rectangle, which is $6 \text{ mm}$.
The height of the triangle is given as $3 \text{ mm}$.
The formula for the area of a triangle is $A_{triangle} = \frac{1}{2} \times \text{base} \times \text{height}$.

$$A_{triangle} = \frac{1}{2} \times 6 \text{ mm} \times 3 \text{ mm}$$ $$A_{triangle} = 3 \text{ mm} \times 3 \text{ mm} = 9 \text{ mm}^2$$

The total area is the sum of the area of the rectangle and the area of the triangle.

$$A_{total} = A_{rectangle} + A_{triangle}$$ $$A_{total} = 24 \text{ mm}^2 + 9 \text{ mm}^2$$ $$A_{total} = 33 \text{ mm}^2$$

The area of the shape is $33 \text{ mm}^2$.