Question

What is the total surface area of the figure?

(1 point)
___________

The first shape has:

Height: 8
Length:10
Width: 6

Second shape:

Height: 6
Length:6
Width:6

Answer 1

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:
\[
\boxed{592}
\]