To find the total surface area of the two shapes, we'll need to calculate the surface area of each shape separately.
Shape 1: Rectangular Prism
Dimensions:
- Height (h): 8
- Length (l): 10
- Width (w): 6
The formula for the surface area \(SA\) of a rectangular prism is: \[ SA = 2(lw + lh + wh) \]
Plugging in the dimensions: \[ SA_1 = 2(10 \cdot 6 + 10 \cdot 8 + 6 \cdot 8) \]
Calculating each term:
- \(lw = 10 \cdot 6 = 60\)
- \(lh = 10 \cdot 8 = 80\)
- \(wh = 6 \cdot 8 = 48\)
Now adding them up: \[ SA_1 = 2(60 + 80 + 48) = 2(188) = 376 \]
Shape 2: Cube
Dimensions:
- Height (h): 6
- Length (l): 6
- Width (w): 6
The formula for the surface area \(SA\) of a cube is: \[ SA = 6s^2 \] where \(s\) is the side length (in this case, all sides are the same).
Plugging in the dimension: \[ SA_2 = 6(6^2) = 6 \cdot 36 = 216 \]
Total Surface Area
Now, we can find the total surface area by adding the surface areas of both shapes: \[ Total SA = SA_1 + SA_2 = 376 + 216 = 592 \]
So, the total surface area of the figure is: \[ \boxed{592} \]