Question

Find the surface area of each figure. A rectangular prism has three pairs of identical faces, so find the area of each and double them.
A=2lw+2wh+2lh
Be sure to subtract the hidden area when the two figures are placed together. Subtract that area from both figures

Answer 1

To find the surface area of a rectangular prism and account for cases where two figures are placed together, we can use the formula for the surface area of a rectangular prism, which is:

\[
A = 2lw + 2wh + 2lh
\]

where:
- \( l \) = length
- \( w \) = width
- \( h \) = height

### Step 1: Calculate the Surface Area of One Rectangular Prism

Let's calculate the surface area for a prism with given dimensions \( l \), \( w \), and \( h \).

Assuming you have specific dimensions, substitute those values into the formula. For example, if:
- \( l = 4 \) units
- \( w = 3 \) units
- \( h = 2 \) units

We can calculate:

\[
A = 2(4)(3) + 2(3)(2) + 2(4)(2)
\]
\[
= 2(12) + 2(6) + 2(8)
\]
\[
= 24 + 12 + 16
\]
\[
= 52 \text{ square units}
\]

### Step 2: Adjust for Two Prisms Placed Together

If you have two identical rectangular prisms placed together, we need to consider the area that is not visible (the hidden area). Assuming the two prisms are placed together along one face, you would need to:
1. Determine the area of the face that is hidden.
2. Subtract that area from the total surface area of both prisms.

For instance, if the two prisms are placed together along the face of \( l \times w \), the hidden area (which we want to subtract) is:

\[
\text{Hidden Area} = lw
\]

### Step 3: Combine the Surface Area of Two Prisms and Subtract Hidden Area

The total surface area for two prisms without considering the hidden area would be:
\[
2A = 2 \times 52 = 104 \text{ square units}
\]

Next, subtract the hidden area:

\[
\text{Adjusted Surface Area} = 2A - \text{Hidden Area}
\]
\[
= 104 - (lw)
\]

Using the values \( l = 4 \) and \( w = 3 \):

\[
\text{Hidden Area} = 4 \times 3 = 12 \text{ square units}
\]

Thus, the surface area of the two prisms placed together would be:

\[
\text{Adjusted Surface Area} = 104 - 12 = 92 \text{ square units}
\]

### Conclusion

The total surface area of the two rectangular prisms placed together, accounting for the hidden area, is \( 92 \) square units.