To find the surface area of this composite object, which consists of two rectangular prisms joined together, follow these steps:

1. Identify the Two Prisms and Their Dimensions:

   • There are two prisms: a vertical prism and a horizontal prism.
   • Vertical Prism dimensions: 40 mm (width) x 60 mm (height) x 60 mm (depth).
   • Horizontal Prism dimensions: 80 mm (width) x 60 mm (height) x 10 mm (depth).

2. Calculate the Surface Area of Each Prism Individually:

   • Use the formula for the surface area of a rectangular prism:
     $\text{Surface Area} = 2lw + 2lh + 2wh$ where $l$ is the length, $w$ is the width, and $h$ is the height.
   • Apply this formula separately for the vertical and horizontal prisms.

3. Subtract the Area of the Overlapping Faces:

   • Since these prisms are connected, the area of the faces that are in contact should be subtracted to avoid double-counting.
   • Determine the area of the overlapping face, which will be the area of one side of the contact face between the two prisms. Assuming the overlap face has dimensions 60 mm by 10 mm, calculate this area.

4. Add the Surface Areas of the Two Prisms and Subtract the Overlap:

   • Once you have the surface areas for each prism, add them together.
   • Then, subtract the area of the overlapping face calculated in Step 3 to get the total surface area of the composite object.

5. Complete the Calculation:

   • Plug in the values and perform the arithmetic to find the total surface area.

Would you like the specific surface area calculations for each prism or any further clarification on these steps?

Here are five questions to expand your understanding:

1. How do you calculate the surface area of a rectangular prism if it has different side lengths?
2. Why do we need to subtract the overlapping area in composite shapes?
3. What would be the impact on the surface area if the prisms were not overlapping?
4. How can we calculate the volume of a composite object with multiple prisms?
5. What are the common errors to watch for when calculating surface areas in composite shapes?

Tip: Always identify and handle overlapping areas carefully when calculating surface areas in composite shapes to avoid overcounting.