To find the area of the composite shape in the image, we will separate it into two simpler shapes: a rectangle and a right triangle.

Step-by-Step Solution:

1. Identify the two shapes:

   • Rectangle: The base of the shape is a rectangle.
   • Right Triangle: The upper portion of the shape forms a right triangle.

2. Dimensions of the Rectangle:

   • Length: $30 \, \text{mm}$
   • Width: $5 \, \text{mm}$

   The area $A_R$ of the rectangle is given by: $A_R = \text{length} \times \text{width} = 30 \times 5 = 150 \, \text{mm}^2$

3. Dimensions of the Right Triangle:

   • Base: $20 \, \text{mm}$ (the horizontal distance on the top right)
   • Height: $7 \, \text{mm}$ (the vertical distance)

   The area $A_T$ of the right triangle is given by: $A_T = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \times 7$

   $A_T = 10 \times 7 = 70 \, \text{mm}^2$

4. Calculate the total area of the composite shape: $\text{Total Area} = A_R + A_T = 150 + 70 = 220 \, \text{mm}^2$

Conclusion:

The area of the composite shape is 220 square millimeters.

Would you like more details or have any questions?

Related Questions:

1. How would you calculate the perimeter of the composite shape?
2. What is the difference in area if the dimensions of the rectangle are doubled?
3. How can you determine the hypotenuse of the right triangle using the given dimensions?
4. How does the shape change if the triangle's base is reduced by half?
5. How would the area change if the shape were scaled by a factor of 2?

Tip:

To simplify calculations, always separate complex shapes into basic geometric figures like rectangles, triangles, and circles. This makes it easier to compute areas and other properties.