Grid of labeled geometric figures showing different 3D shapes with their dimensions.

Based on the image you provided, it appears to be a matching exercise. You are likely asked to match each 3D shape (labeled A through L) with its correct volume from the list of values shown at the bottom (e.g., 380 cm³, 127 cm³, 84 cm³, etc.).

Since the full list of volumes is partially cut off in your image, I will calculate the volume for each shape A–L using standard geometric formulas. Then, you can match them to the given volume options.

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📐 Volume Formulas Used:

- Rectangular Prism (Cuboid): `V = length × width × height`
- Triangular Prism: `V = (base area of triangle) × depth`
→ Base area of triangle = `(1/2) × base × height`
- Trapezoidal Prism: `V = (average of parallel sides × height of trapezoid) × depth`

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## 🔢 Calculations for Each Shape:

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A. Square-based Rectangular Prism

Dimensions: 5 cm × 6 cm × 5 cm?
Wait — labeled as “Square-based”, but dimensions are 5 cm, 6 cm — probably typo or mislabel.
Assuming it’s a rectangular prism with dimensions: 5 cm × 6 cm × 5 cm?
Actually, looking at the drawing, it's likely 5 cm × 6 cm × 5 cm, but that’s not square-based.

Re-examining: The front face is shaded and looks like 5 cm × 5 cm? But side says 6 cm.
Let’s assume dimensions are: length=5 cm, width=6 cm, height=5 cm → Not square-based.
But label says "Square-based", so perhaps base is 5 cm × 5 cm, height 6 cm?

✔ Let’s go with: Base = 5 cm × 5 cm, Height = 6 cm
→ `V = 5 × 5 × 6 = 150 cm³`

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B. Rectangular Prism

Dimensions: 2 cm × 3 cm × 8 cm
→ `V = 2 × 3 × 8 = 48 cm³`

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C. Rectangular Prism

Dimensions: 7 cm × 8 cm × 4 cm
→ `V = 7 × 8 × 4 = 224 cm³`

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D. Triangular Prism

Triangle base: right triangle with legs 3 cm and 4 cm
→ Area = `(1/2) × 3 × 4 = 6 cm²`
Depth (prism length) = ? Not labeled! But from shape, it looks like depth is 5 cm? Wait — no label.

Looking closely — the triangular face has base 4 cm, height 3 cm. The depth (into page) is not labeled. This is a problem.

Wait — in many such diagrams, if only two dimensions are given for the triangle and one for depth, we assume the third dimension is the depth. But here, only 3 cm and 4 cm are labeled on the triangle. No depth given.

This may be an error, or perhaps depth is implied. Let’s assume depth = 5 cm (common in such problems).

→ `V = (1/2 × 3 × 4) × 5 = 6 × 5 = 30 cm³`

But let’s hold off — maybe later shapes clarify.

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E. Triangular Prism

Triangle: base 8 cm, height 9 cm? But there’s a small rectangle drawn inside — likely indicating the prism depth.

Actually, the triangle has base 8 cm, height 9 cm, and the depth (perpendicular to triangle) is 2 cm (labeled).

→ Area of triangle = `(1/2) × 8 × 9 = 36 cm²`
→ `V = 36 × 2 = 72 cm³`

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F. Triangular Prism

Triangle: right triangle, legs 5 cm and 6 cm?
Wait — labeled: vertical leg 5 cm, horizontal leg 6 cm, hypotenuse 7 cm (which checks: 5-6-7? 5²+6²=25+36=61 ≠ 49 → not right triangle? Mistake?)

Actually, 5-6-7 is not a right triangle. But there’s a right angle symbol at the corner of 5 cm and 6 cm — so it *is* a right triangle.

Then hypotenuse should be √(25+36)=√61≈7.8 — but labeled 7 cm. Inconsistency.

Probably, ignore hypotenuse label — use legs 5 cm and 6 cm for area.

Area = `(1/2) × 5 × 6 = 15 cm²`
Depth = ? Not labeled. Looking at diagram, the depth seems to be 5 cm (same as vertical leg?).

Actually, the depth is perpendicular to the triangle — likely 5 cm (labeled on the side).

→ `V = 15 × 5 = 75 cm³`

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G. Triangular Prism

Triangle: base 8 cm, height 9 cm? But again, there’s a depth labeled 5 cm.

Area = `(1/2) × 8 × 9 = 36 cm²`
Depth = 5 cm
→ `V = 36 × 5 = 180 cm³`

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H. Triangular Prism

Triangle: equilateral? Sides 6 cm, 6 cm, 5 cm? Not equilateral.

Actually, it’s a triangle with base 6 cm, and height? Not labeled. But there’s a 5 cm side.

Wait — the triangle has two sides 6 cm and base 5 cm? Or is it base 6 cm, height 5 cm?

Looking at diagram: the shaded triangle has base 6 cm, and height (perpendicular) is 5 cm (labeled).

→ Area = `(1/2) × 6 × 5 = 15 cm²`
Depth = ? Not labeled. But from shape, depth might be 6 cm? Labeled on side.

Actually, the depth (into page) is labeled 6 cm on the vertical edge.

→ `V = 15 × 6 = 90 cm³`

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I. Trapezoidal Prism

Trapezoid: parallel sides 5 cm and 10 cm, height 3 cm
→ Area = `(1/2) × (5 + 10) × 3 = (1/2) × 15 × 3 = 22.5 cm²`
Depth = 7 cm (labeled on slanted side? Actually, the depth is perpendicular to trapezoid — likely 7 cm)

→ `V = 22.5 × 7 = 157.5 cm³`

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J. Trapezoidal Prism

Trapezoid: parallel sides 4 cm and 9 cm, height 5 cm?
Wait — labeled: left side 4 cm, right side 9 cm, depth 10 cm, and top/bottom?

Actually, the trapezoid has bases 4 cm and 9 cm, height 5 cm (vertical distance between them).
→ Area = `(1/2) × (4 + 9) × 5 = (1/2) × 13 × 5 = 32.5 cm²`
Depth = 10 cm
→ `V = 32.5 × 10 = 325 cm³`

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K. Trapezoidal Prism

Trapezoid: parallel sides 5 cm and 9 cm, height 7 cm?
Wait — labeled: top 5 cm, bottom 9 cm, height 7 cm (vertical), and depth 4 cm.

→ Area = `(1/2) × (5 + 9) × 7 = (1/2) × 14 × 7 = 49 cm²`
Depth = 4 cm
→ `V = 49 × 4 = 196 cm³`

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L. Triangular Prism

Triangle: base 7 cm, height 9 cm? But labeled 3 cm on side.

Actually, the triangle has base 7 cm, height 9 cm? But there’s a 3 cm label on the side — likely the depth.

Wait — the shaded face is a triangle with base 7 cm, and height 9 cm (vertical). The depth (into page) is 3 cm.

→ Area = `(1/2) × 7 × 9 = 31.5 cm²`
Depth = 3 cm
→ `V = 31.5 × 3 = 94.5 cm³`

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## ✔ Summary of Volumes:

| Shape | Volume (cm³) |
|-------|--------------|
| A | 150 |
| B | 48 |
| C | 224 |
| D | 30* |
| E | 72 |
| F | 75 |
| G | 180 |
| H | 90 |
| I | 157.5 |
| J | 325 |
| K | 196 |
| L | 94.5 |

*Note: For D, assumed depth = 5 cm due to missing label.*

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## 🔄 Matching to Given Volumes (from bottom of image):

You mentioned volumes like:
- 380 cm³
- 127 cm³
- 84 cm³
- 101 cm³

These don’t exactly match our calculated volumes. Perhaps:

- Maybe some shapes are combined?
- Or perhaps I misinterpreted depths?
- Or the volumes listed are for different groupings?

Alternatively, maybe the volumes at the bottom are answers to match, and you need to pick which shape corresponds to which volume.

For example:

- If 380 cm³ is an option, none of our shapes reach that — unless J is miscalculated.

Let’s recheck J:

> J: Trapezoid with bases 4 cm and 9 cm, height 5 cm → area = (4+9)/2 * 5 = 65/2 = 32.5 → times depth 10 = 325 — correct.

What if depth is 12 cm? Labeled “12 cm” on the vertical side — maybe that’s the depth?

In J, the 12 cm is labeled on the vertical edge — that’s likely the height of the trapezoid, not the depth.

The depth is labeled 10 cm on the base.

So 325 cm³ is correct.

Perhaps the volumes at the bottom are not all for A-L, or maybe it’s a different set.

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## 💡 Recommendation:

Since the full list of target volumes is cut off, and some dimensions are ambiguous (like in D, F, J), the best approach is:

1. Use the calculations above to find each volume.
2. Match them to the closest given volume in your worksheet.
3. If you can provide the full list of volume options (the ones at the bottom), I can give you the exact matching.

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## 🧩 Example Matching (if volumes were: 48, 72, 75, 90, 150, 180, 196, 224, 325...)

Then:
- A → 150
- B → 48
- C → 224
- D → 30 (if available)
- E → 72
- F → 75
- G → 180
- H → 90
- I → 157.5 (round to 158?)
- J → 325
- K → 196
- L → 94.5

If 380 cm³ is listed, it might be a mistake or for a different shape.

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## ✔ Final Answer:

Without the complete list of target volumes, here are the calculated volumes for each shape:

- A: 150 cm³
- B: 48 cm³
- C: 224 cm³
- D: 30 cm³ (assuming depth = 5 cm)
- E: 72 cm³
- F: 75 cm³
- G: 180 cm³
- H: 90 cm³
- I: 157.5 cm³
- J: 325 cm³
- K: 196 cm³
- L: 94.5 cm³

Please provide the full list of volume options from the bottom of the image, and I’ll give you the exact matching pairs!

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Let me know if you want help matching these to specific numbers once you share the full list!