Question

Use the image to answer the question.An illustration shows a three dimensional composite figure formed by a smaller rectangular prism connected to a larger rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism on the left has a length of 10 millimeters a height of 8 millimeters. The width of the rectangular prism is not shown, but it aligns perfectly with the width of the rectangular prism on the right. The rectangular prism on the right has a length of 6 millimeters, a width of 6 millimeters, and a height 6 of millimeters. The combined length of the two rectangular prisms measures 16 millimeters. What is the total surface area of the figure?(1 point)

Answer 1

wrong

Answer 2

To calculate the total surface area of the composite figure comprising two rectangular prisms, we can follow the steps outlined below:

1. **Identify Dimensions of Each Prism:**
- For the smaller rectangular prism (left):
- Length (L1) = 10 mm
- Height (H1) = 8 mm
- Width (W1) can be calculated as follows:
Since the combined length of both prisms is 16 mm and the length of the larger prism (right) is 6 mm:
\[
W1 = W2 = 6 \text{ mm} \quad (\text{as they align perfectly})
\]
- For the larger rectangular prism (right):
- Length (L2) = 6 mm
- Width (W2) = 6 mm
- Height (H2) = 6 mm

2. **Calculate the Surface Area of Each Prism:**
- The surface area \( S \) of a rectangular prism can be calculated as:
\[
S = 2(L \times W + L \times H + W \times H)
\]
- **Surface Area of the smaller prism (left):**
\[
S1 = 2(10 \times 6 + 10 \times 8 + 6 \times 8)
\]
\[
S1 = 2(60 + 80 + 48) = 2(188) = 376 \text{ mm}^2
\]

- **Surface Area of the larger prism (right):**
\[
S2 = 2(6 \times 6 + 6 \times 6 + 6 \times 6)
\]
\[
S2 = 2(36 + 36 + 36) = 2(108) = 216 \text{ mm}^2
\]

3. **Adjust for Overlapping Area:**
- Since the two prisms are connected, they share a face. The shared area is part of the surface area of both prisms and thus, it must be subtracted:
- The area of the shared face is the area of the base (width * height) of the smaller prism, which aligns with the width of the shared face:
\[
\text{Shared Area} = W1 \times H1 = 6 \times 8 = 48 \text{ mm}^2
\]

4. **Calculate the Total Surface Area:**
- Combining the surface areas and subtracting the shared area:
\[
\text{Total Surface Area} = S1 + S2 - \text{Shared Area}
\]
\[
\text{Total Surface Area} = 376 + 216 - 48 = 544 \text{ mm}^2
\]

Thus, the total surface area of the composite figure is **544 mm²**.