Composite rectangular prism with dimensions 13 x 6 x 5 and a 5 x 5 x 5 cube on top.

It looks like you've uploaded an image of a 3D composite shape made up of two rectangular prisms (cuboids) joined together. Let's analyze and solve the problem step by step.

Step 1: Understand the Shape

From the diagram:

- There is a larger rectangular prism at the base.
- On top of it, to the right, there is a smaller cube-like prism sitting on top.
- Dimensions are labeled:
- The base has:
- Length = 13
- Height = 6
- Depth (width) = 5
- The top smaller block has:
- Length = 5
- Height = 5
- Depth (width) = 5

So both blocks have a depth (width) of 5 units.

Step 2: Determine What Is Being Asked

Since no specific question was stated in your message, I’ll assume common problems associated with such diagrams:

#### Likely Problem: Find the total surface area of the composite solid.

Alternatively, it could be asking for volume, but surface area is more typical when given this kind of diagram.

Let’s solve for surface area, as it's more complex and likely intended.

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Step 3: Surface Area Calculation

We need to compute the total surface area of the combined shape, subtracting overlapping areas where the two blocks touch.

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#### A. Surface Area of the Larger Base Prism

Dimensions:
- Length = 13
- Width = 5
- Height = 6

Surface area of a rectangular prism:
$$
SA = 2(lw + lh + wh)
$$
$$
= 2(13 \cdot 5 + 13 \cdot 6 + 5 \cdot 6) = 2(65 + 78 + 30) = 2(173) = 346
$$

But we must subtract the area of the face that is covered by the smaller block.

The smaller block sits on top of the larger one, so the bottom face of the small block covers part of the top face of the large block.

Area of contact = $5 \times 5 = 25$

So, we subtract this from the large block's surface area twice? No — actually:

Wait! We only subtract once from the large block, because its top face loses 25 square units of exposed area.

And we also subtract the bottom face of the small block (which is not exposed), so we don’t count it.

So total surface area = (surface area of large) + (surface area of small) – 2 × overlapping area (because both the top of the large and bottom of the small lose exposure).

But wait: when two faces are glued together, both are no longer exposed, so we subtract twice the overlapping area.

Yes.

So:

- SA of large = 346
- SA of small = ?

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#### B. Surface Area of the Small Top Block

Dimensions: 5 × 5 × 5 → it's a cube!

SA of cube = $6 \times (5)^2 = 6 \times 25 = 150$

But again, the bottom face (5×5 = 25) is glued to the large block, so not exposed.

So we subtract 25 from its surface area.

So effective SA contribution from small block = $150 - 25 = 125$

But wait — better approach: total SA = SA_large + SA_small − 2×(contact area)

Because:
- Large block loses 25 from its top
- Small block loses 25 from its bottom
→ Total reduction: 50

So:

Total surface area = $346 + 150 - 2 \times 25 = 496 - 50 = 446$

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✔ Final Answer: Total Surface Area = 446 square units

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Alternative: Volume?

If instead the task was to find volume, then:

- Volume of large block = $13 \times 5 \times 6 = 390$
- Volume of small block = $5 \times 5 \times 5 = 125$
- Total volume = $390 + 125 = 515$ cubic units

But since the image shows dimensions and a composite shape, surface area is more likely.

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Conclusion

Assuming the problem asks for total surface area, the answer is:

> 446 square units

If you meant something else (e.g., volume, or perimeter, or net), please clarify.

Let me know if you'd like a visual breakdown or explanation of how the surfaces overlap.