Geometry worksheet practicing identification and measurement of 3D solids and their 2D nets.

Let's solve each problem step by step. The task is to match the 3D solid with its corresponding net and fill in the missing dimensions on the nets based on the given solid.

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🔷 Problem 1: Rectangular Prism

#### ✔ Solid:
- Dimensions:
- Length = 8 cm
- Width = 6 cm
- Height = 5 cm

This is a rectangular prism (box shape).

#### ✔ Net:
The net should have:
- 2 faces of size 8 cm × 6 cm (top and bottom)
- 2 faces of size 8 cm × 5 cm (front and back)
- 2 faces of size 6 cm × 5 cm (left and right)

Looking at the net:

- There are two rectangles labeled 8 cm and 5 cm → these must be the front/back (8×5)
- One rectangle labeled 6 cm and 5 cm → this is side face
- Other parts need to be filled in.

Let’s label the blanks:

- Top left rectangle: height = 6 cm, width = ? → must be 8 cm (since it connects to 8 cm side)
- Middle horizontal rectangle: 8 cm × 5 cm → already labeled
- Below that: another rectangle with height 5 cm → must be 8 cm wide
- Right side: vertical rectangle connected to 8 cm → must be 6 cm high? Wait — let's analyze carefully.

Actually, the net layout shows:

```
[6cm] [___] [___]
| |
[5cm][8cm]
| |
[___] [___]
```

Wait, better to reconstruct the net.

From the image:
- Top row: one rectangle is 6 cm high, and next to it is an unlabeled rectangle.
- Then below, there's a central rectangle labeled 8 cm and 5 cm.
- Two rectangles below that, each labeled with ___ cm.
- On the right side, three rectangles stacked vertically with labels like ___ cm.

But looking closely:

It appears the net has:
- A central rectangle: 8 cm × 5 cm (likely front or back)
- Attached to it: top and bottom rectangles (height 5 cm), so they must be 8 cm wide → so their length is 8 cm
- Left and right rectangles: attached to sides, but the left one has 6 cm marked vertically → so that's the depth
- So the side faces are 6 cm × 5 cm → so those rectangles are 6 cm wide

Now fill in:

- Top rectangle: 6 cm high → must be 8 cm long → so write 8 cm
- Bottom rectangle: same → 8 cm
- Left rectangle: 6 cm high → so it must be 5 cm wide? No — wait.

Wait — let's look at the connections.

Better approach:

The net has:
- Central rectangle: 8 cm (horizontal) × 5 cm (vertical)
- Above and below it: rectangles that are 5 cm tall → so if they are attached along the 8 cm edge, then their width is 8 cm
- To the left and right: rectangles attached along the 5 cm edge → so they must be 6 cm wide (since the depth is 6 cm)

So:
- The top and bottom rectangles: 8 cm × 5 cm → so the blank for width is 8 cm
- The left and right rectangles: 6 cm × 5 cm → so the blank for width is 6 cm

But in the net:
- The top rectangle: has 6 cm on the left side → that’s the height → so it’s 6 cm tall → but wait, that contradicts.

Wait — recheck the image.

In the net:
- The top rectangle has 6 cm on the left side → so it's 6 cm high
- It's adjacent to a rectangle labeled 8 cm and 5 cm, which is 8 cm wide and 5 cm tall

Ah! So the 6 cm is the depth, not height.

So:

- The top rectangle: 6 cm × 8 cm → because it's attached to the 8 cm side → so it must be 8 cm long
- Similarly, the bottom rectangle: also 6 cm × 8 cm → so 8 cm
- The side rectangles: attached to the 5 cm side → so they must be 5 cm wide → but we know the depth is 6 cm → no

Wait — confusion arises.

Let’s define:

For a rectangular prism with:
- Length = 8 cm
- Width = 6 cm
- Height = 5 cm

Then the faces are:
- 2 of 8×6 (top/bottom)
- 2 of 8×5 (front/back)
- 2 of 6×5 (sides)

Now look at the net:

It has:
- One rectangle: 8 cm × 5 cm → labeled
- Above it: a rectangle with 6 cm on the side → so this must be a 6 cm × 8 cm face? But 6 cm is height, 8 cm is width → yes

Wait — the rectangle above the 8×5 has a side labeled 6 cm → so that’s its height → so it's 6 cm high → and since it's attached along the 8 cm side, it must be 8 cm wide → so it's 8 cm × 6 cm → correct (top face)

Similarly, below the 8×5 rectangle: another rectangle with 6 cm on the side → so it's 8 cm × 6 cm → bottom face

Then on the right side: a rectangle attached to the 5 cm side → so it must be 5 cm wide → and since the depth is 6 cm, it should be 6 cm tall → so it's 6 cm × 5 cm → side face

So:

Fill in the blanks:

- Top rectangle: has 6 cm on the left → so the horizontal dimension is 8 cm
- The rectangle to the right of the 8×5: it's attached to the 5 cm side → so its height is 5 cm → and it's 6 cm wide → so the blank on the right side is 6 cm
- The rectangle below the 8×5: labeled 5 cm on the left → so it's 5 cm high → and width is 8 cm → so blank is 8 cm
- The rectangle to the right of that: again, attached to 5 cm → so it's 6 cm wide → blank is 6 cm

Wait — actually, the net has:

- Top rectangle: 6 cm (height), blank width → must be 8 cm
- Middle rectangle: 8 cm × 5 cm
- Bottom rectangle: 5 cm (height), blank width → must be 8 cm
- Right column: two rectangles stacked vertically → both have blank widths → they are attached to the 5 cm side → so they are 5 cm high → and width = 6 cm → so blank is 6 cm

But in the net, the rightmost rectangles are labeled with "___ cm" on the right side → so we fill in the length of those rectangles.

So:

- Top rectangle: width = 8 cm
- Bottom rectangle: width = 8 cm
- Right side rectangles: each has width = 6 cm

Also, the middle rectangle has 8 cm and 5 cm → already labeled

And the small rectangles on the right: one has 5 cm (height), so it's 6 cm wide → so the blank on the right is 6 cm

So final answers for Problem 1:

- Top rectangle: 8 cm
- Bottom rectangle: 8 cm
- Right side rectangles: 6 cm (each)
- Also, the left side rectangle: has 6 cm on the left → so its width is 5 cm? Wait — no.

Wait — the left side rectangle is connected to the 5 cm side of the 8×5 rectangle → so it's 5 cm wide → and 6 cm tall → so its width (horizontal) is 5 cm

But in the net, the left rectangle has a blank on the left side → it says "___ cm" → so that’s the horizontal dimension → must be 5 cm

Wait — let’s clarify:

Looking at the net:

```
[6 cm] [______] [______]
| |
[5 cm][8 cm]
| |
[______] [______]
```

No — actually, the drawing is:

- Top row: one rectangle with 6 cm on the left side, and a blank on the right
- Then below: a rectangle with 5 cm and 8 cm
- Then below that: two rectangles, each with blank on the right

But actually, from the image:

The net has:
- A large rectangle in the center: 8 cm (horizontal) × 5 cm (vertical)
- Above it: a rectangle with 6 cm on the left side → so this rectangle is 6 cm tall, and attached along the 8 cm side → so its width is 8 cm → so blank is 8 cm
- Below it: another rectangle with 5 cm on the left → so it's 5 cm tall → and width is 8 cm → so blank is 8 cm
- To the right: two rectangles stacked vertically → each has a blank on the right side → they are attached to the 5 cm side → so they are 5 cm tall → and width = 6 cm → so blank is 6 cm
- To the left: one rectangle → has blank on the left → it's attached to the 5 cm side → so it's 5 cm tall → and width = 6 cm → so blank is 6 cm

Wait — no: the left rectangle is attached to the 5 cm side of the central rectangle → so it must be 5 cm wide → and 6 cm tall → so its width (horizontal) is 5 cm

But the blank is on the left side → that’s the vertical dimension?

Wait — the label "___ cm" is on the side of the rectangle.

So:
- For the top rectangle: left side is labeled 6 cm → so height is 6 cm → width is 8 cm → so the blank on the right side is 8 cm
- For the bottom rectangle: left side is labeled 5 cm → so height is 5 cm → width is 8 cm → blank on the right is 8 cm
- For the right side rectangles: each has a blank on the right → so that’s the horizontal dimension → must be 6 cm (since depth is 6 cm)
- For the left rectangle: blank on the left → that’s the vertical dimension → but it’s attached to the 5 cm side → so it must be 5 cm tall → so blank is 5 cm

But wait — the left rectangle is attached to the 5 cm side of the central rectangle → so its height is 5 cm → so blank on the left is 5 cm

But the left rectangle is not labeled with a number — only the blank is there.

So final fills for Problem 1:

- Top rectangle: right side blank → 8 cm
- Bottom rectangle: right side blank → 8 cm
- Right side rectangles: right side blanks → 6 cm each
- Left rectangle: left side blank → 5 cm

But in the net, the left rectangle is drawn with a blank on the left side → so that’s the vertical dimension → must be 5 cm

Yes.

So answers:

- Top: 8 cm
- Bottom: 8 cm
- Right: 6 cm
- Left: 5 cm

✔ Answer 1:
- Top rectangle: 8 cm
- Bottom rectangle: 8 cm
- Right rectangles: 6 cm
- Left rectangle: 5 cm

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🔷 Problem 2: Triangular Prism

#### ✔ Solid:
- Triangle base: base = 4 cm, height = 5 cm
- Side length (length of prism) = 7 cm
- The two triangular ends are equilateral? No — just a triangle with base 4 cm, height 5 cm
- The three rectangular faces: each has width = 7 cm
- The lengths of the triangle sides: we see one side is 5 cm (the slant), base is 4 cm, and the other side is unknown? But in the net, it's labeled as 5 cm

Wait — the solid shows:
- Triangle: base = 4 cm, height = 5 cm
- The two equal sides are labeled 5 cm → so it's an isosceles triangle with two sides 5 cm, base 4 cm
- The prism extends 7 cm → so lateral edges are 7 cm

So the net should have:
- 2 triangles: base 4 cm, height 5 cm, sides 5 cm
- 3 rectangles: all 7 cm wide
- One rectangle: 7 cm × 4 cm (attached to base)
- Two rectangles: 7 cm × 5 cm (attached to the equal sides)

Now look at the net:

- Central rectangle: 7 cm × ___ → must be 7 cm × 5 cm? But it’s labeled 7 cm on the side → so height is 7 cm
- Top and bottom: triangles with 5 cm labeled → so sides are 5 cm
- Left and right: rectangles attached to the 5 cm sides → so they are 7 cm × 5 cm → so width is 5 cm
- But the central rectangle is attached to the 4 cm base → so it must be 7 cm × 4 cm → so its width is 4 cm

Wait — in the net:
- The central rectangle has 7 cm on the side → so height is 7 cm
- Its width is blank → must be 4 cm (base of triangle)
- Left and right rectangles: attached to the 5 cm sides → so they are 7 cm × 5 cm → so their width is 5 cm
- Top and bottom triangles: already labeled 5 cm (sides)

So blanks:
- Central rectangle: width = 4 cm
- Left rectangle: width = 5 cm
- Right rectangle: width = 5 cm
- Top triangle: already labeled
- Bottom triangle: already labeled

But in the net:
- The left rectangle has a blank on the left → that’s the width → so 5 cm
- The right rectangle has a blank on the right → width → 5 cm
- The central rectangle has a blank on the top → that’s the width → 4 cm

So:

✔ Answer 2:
- Central rectangle: 4 cm
- Left rectangle: 5 cm
- Right rectangle: 5 cm

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🔷 Problem 3: Cube

#### ✔ Solid:
- All sides = 3 cm → cube

#### ✔ Net:
- Must be 6 squares, each 3 cm × 3 cm
- The net shown is a cross-shaped net with one square in the center, four around it, and one on the side

All rectangles are labeled with 3 cm on some sides → so we need to fill in the missing dimensions

Each face is 3 cm × 3 cm

So any blank side must be 3 cm

Look at the net:

- Horizontal row: five rectangles → all should be 3 cm wide
- Vertical: one on the right → 3 cm high
- Blanks:
- Top rectangle: left side blank → must be 3 cm
- Second rectangle: left side blank → 3 cm
- Third rectangle: left side blank → 3 cm
- Fourth rectangle: left side blank → 3 cm
- Right rectangle: top side blank → 3 cm
- Bottom rectangle: left side blank → 3 cm

Wait — in the net:

- The top rectangle: has 3 cm on the right → so width is 3 cm → blank on the left → must be 3 cm
- Second rectangle: 3 cm on the right → so blank on the left → 3 cm
- Third rectangle: 3 cm on the right → blank on the left → 3 cm
- Fourth rectangle: 3 cm on the right → blank on the left → 3 cm
- Fifth rectangle: 3 cm on the right → blank on the left → 3 cm
- Right rectangle: has 3 cm on the bottom → so height is 3 cm → blank on the top → 3 cm
- Bottom rectangle: has 3 cm on the right → so width is 3 cm → blank on the left → 3 cm

So all blanks are 3 cm

✔ Answer 3:
All blanks = 3 cm

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✔ Final Answers:

#### Problem 1:
- Top rectangle: 8 cm
- Bottom rectangle: 8 cm
- Left rectangle: 5 cm
- Right rectangles: 6 cm each

#### Problem 2:
- Central rectangle: 4 cm
- Left rectangle: 5 cm
- Right rectangle: 5 cm

#### Problem 3:
- All blanks: 3 cm

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📝 Summary Table:

| Problem | Missing Dimensions |
|--------|---------------------|
| 1 | Top: 8 cm, Bottom: 8 cm, Left: 5 cm, Right: 6 cm |
| 2 | Central: 4 cm, Left: 5 cm, Right: 5 cm |
| 3 | All blanks: 3 cm |

Let me know if you'd like a visual explanation or diagram!