To find the total surface area of the two solid shapes, we'll start by calculating the surface area of each rectangular prism, then subtract the area of the face where they connect.
Step 1: Calculate the Surface Area of Each Figure
First Shape: Rectangular Prism 1
- Height (h1): 8
- Length (l1): 10
- Width (w1): 6
Using the formula for surface area: \[ A_1 = 2lw + 2wh + 2lh \] Calculating each term:
- \(2lw = 2 \times 10 \times 6 = 120\)
- \(2wh = 2 \times 6 \times 8 = 96\)
- \(2lh = 2 \times 10 \times 8 = 160\)
Adding these up: \[ A_1 = 120 + 96 + 160 = 376 \]
Second Shape: Rectangular Prism 2
- Height (h2): 6
- Length (l2): 6
- Width (w2): 6
Using the same formula for surface area: \[ A_2 = 2lw + 2wh + 2lh \] Calculating each term:
- \(2lw = 2 \times 6 \times 6 = 72\)
- \(2wh = 2 \times 6 \times 6 = 72\)
- \(2lh = 2 \times 6 \times 6 = 72\)
Adding these up: \[ A_2 = 72 + 72 + 72 = 216 \]
Step 2: Calculate the Hidden Area
When the two prisms are placed together, we assume the faces that touch do not contribute to the outer surface area. The hidden area is the area of the face where the two prisms connect.
Assuming they connect face-to-face on one of the dimensions (for example, on the width of the first prism and the width of the second prism), the hidden area can be calculated based on the shape's dimensions.
For simplicity, assume they are resting on the base together.
Let's assume they are standing on their lengths and widths touching, we'll consider the two widths:
- Width of first prism = 6
- Width of second prism = 6
If they are touching perfectly aligning one square face (both 6 units), The hidden area becomes: \[ \text{Hidden area} = w1 \times h1 = 6 \times 6 = 36 \]
Step 3: Calculate Total Surface Area
Now, the total surface area would be the sum of both surface areas minus the hidden area: \[ \text{Total Surface Area} = A_1 + A_2 - \text{Hidden Area} \] Calculating this: \[ \text{Total Surface Area} = 376 + 216 - 36 = 556 \]
Final Answer:
The total surface area of the figure is 556 square units.