Worksheet for drawing 3D shapes on an isometric grid.

Let’s solve this step by step.

We are asked to draw two 3D shapes — a cube and a cuboid — from two different perspectives, using the isometric grid (the dotted paper). We must use a ruler for accuracy.

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Step 1: Understand what “two different perspectives” means

In isometric drawing, we usually show 3D shapes with three visible faces: front, top, and side. But “different perspectives” can mean:

- Rotating the shape slightly so you see different sides.
- Or changing which corner or edge is closest to the viewer.

For example:
- For the cube, one view might show the top face clearly, another might tilt it so you see more of the front and side.
- Same for the cuboid — maybe one view shows its length, another shows its height or width more prominently.

But since we’re on an isometric grid, we’ll keep the angles consistent (all lines at 30° or vertical), just change orientation.

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Step 2: Draw the Cube – First Perspective (already done)

The first cube is drawn as a standard isometric cube:
→ All edges equal.
→ Three faces visible: top, front-right, front-left.
→ Each face is a rhombus made of equilateral triangles on the dot grid.

Now we need to draw the same cube but from a different angle.

How? Let’s rotate it mentally.

Instead of having the top face pointing up, let’s make the front face point more toward us — like tipping the cube forward slightly.

On the isometric grid, that means:

- Start with a vertical line (height).
- From the bottom, go diagonally down-left and down-right for depth and width.
- Connect the tops accordingly.

Actually, in true isometric projection, there are only limited orientations. So perhaps “different perspective” here means flipping the cube so that instead of seeing the top, you see the bottom — or rotating it 90 degrees around the vertical axis.

Let’s try this:

#### Second perspective for cube:
Imagine looking at the cube from the opposite corner — so now the face that was hidden becomes visible.

You can draw it like this:

- Start with a dot.
- Go up 4 dots (for height).
- From the bottom dot, go diagonally right-down 4 dots (width).
- From the same bottom dot, go diagonally left-down 4 dots (depth).
- Then connect the ends to form the other corners.
- Finish by connecting all corresponding points.

This will give you a cube that looks “tilted” differently — still accurate, just viewed from another angle.

✔ Important: Keep all edges the same length (e.g., 4 units long on the grid).

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Step 3: Draw the Cuboid – First Perspective (already done)

The given cuboid is longer than it is tall or deep — like a brick lying flat.

Dimensions (approximate from image):

- Length: 6 units (along the diagonal)
- Width: 2 units (other diagonal)
- Height: 2 units (vertical)

Now draw the same cuboid from a different perspective.

Again, rotate it mentally.

Option: Stand the cuboid upright — so now its height becomes the longest dimension.

So instead of lying flat, it stands vertically.

Draw it like this:

- Vertical lines = 6 units high.
- Base: 2 units wide and 2 units deep (on the diagonals).
- Top matches base.

That gives you a tall box — same volume, different orientation.

Alternatively, lay it on its side — so the 6-unit side goes left-right instead of front-back.

Either way, as long as dimensions stay the same and it's drawn accurately on the isometric grid, it counts as a different perspective.

✔ Use your ruler! Count dots carefully.

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Final Check:

Did we draw each shape twice?

✔️ Cube: original + rotated version
✔️ Cuboid: original + reoriented version

Are they accurate? Yes — if we used the grid correctly and kept proportions.

Did we use two different views per shape? Yes — changed orientation without changing size.

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Final Answer:

To complete Task 1:

1. Cube – Second View: On the blank isometric grid, draw a cube where the front face is more prominent — start with a vertical line, then extend diagonals for width and depth, ensuring all edges are equal (e.g., 4 dots long). Connect corners to form 3 visible faces.

2. Cuboid – Second View: Redraw the cuboid standing upright — make the vertical edges 6 dots long, while keeping width and depth at 2 dots each. This changes the perspective from “lying down” to “standing up”.

Use a ruler to ensure straight lines and accurate measurements on the dot grid. Both drawings should look like the same object, just turned to show a different angle.