Cross Sections of 3-D Figures worksheet for identifying shapes formed by slicing solids.

Let’s go through each 3D figure one by one and decide what the cross section looks like when you slice it either parallel to the base or perpendicular to the base.

We’ll use simple logic:
- If you slice parallel to the base, you’re cutting straight across, like slicing a loaf of bread — you get a shape that matches the base.
- If you slice perpendicular to the base, you’re cutting straight down from top to bottom — you usually get a rectangle or triangle, depending on the shape.

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Row 1:

Figure 1: Square pyramid (base is square)
→ Slice parallel to base: You get a smaller square. ✔
→ Slice parallel to base (second box): Also a square — same as above.
→ Slice perpendicular to base: You cut from tip down through center → you get a triangle. ✔

Figure 2: Rectangular prism (like a box)
→ Slice parallel to base: Same rectangle as base. ✔
→ Slice parallel to base (second box): Still a rectangle.
→ Slice perpendicular to base: Cut vertically → still a rectangle (since sides are flat). ✔

Figure 3: Triangular prism (triangle bases)
→ Slice parallel to base: Triangle. ✔
→ Slice parallel to base (second box): Still triangle.
→ Slice perpendicular to base: Cut straight down → you get a rectangle (because the sides are rectangles). ✔

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Row 2:

Figure 4: Cylinder
→ Slice perpendicular to base: Cut straight down → rectangle (if you unroll the side, but in cross section, it’s a rectangle with curved ends? Wait — no! Actually, if you slice perpendicular to the circular base, you get a rectangle only if you cut along the height — but technically, for a cylinder, slicing perpendicular to the base gives a rectangle ONLY if you cut vertically through the axis. But actually, standard answer: slicing perpendicular to base of cylinder = rectangle. Let me double-check: Yes — imagine cutting a soda can straight down from top to bottom — you get a rectangle. ✔
→ Slice parallel to base: Circle. ✔
→ Slice perpendicular to base (third box): Again, rectangle. ✔

Wait — let’s be precise:

Actually, for cylinder:
- Parallel to base → circle
- Perpendicular to base → rectangle (if cut vertically through center)

Yes.

Figure 5: Rectangular prism again (flat one)
→ Slice parallel to base: Rectangle. ✔
→ Slice parallel to base (second box): Rectangle.
→ Slice perpendicular to base: Rectangle (cutting down through height). ✔

Figure 6: Square pyramid again
→ Slice perpendicular to base: Triangle (from apex to base edge). ✔
→ Slice parallel to base: Smaller square. ✔
→ Slice perpendicular to base (third box): Triangle again. ✔

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Row 3:

Figure 7: Cone
→ Slice parallel to base: Circle (smaller than base). ✔
→ Slice parallel to base (second box): Circle.
→ Slice perpendicular to base: Triangle (from tip to base diameter). ✔

Figure 8: Triangular prism (lying on rectangular face?)
Wait — this looks like a triangular prism where the triangular faces are on the ends, and we’re looking at it from the side.
→ Slice parallel to base: The base here is probably the triangle — so parallel slice = triangle. ✔
→ Slice parallel to base (second box): Triangle.
→ Slice perpendicular to base: Cut straight down → rectangle (since the sides are rectangles). ✔

But wait — in the diagram, Figure 8 shows a prism with triangular bases on left/right, and we’re viewing it from front. So “base” likely means the triangular face. So:

- Parallel to base → triangle
- Perpendicular to base → rectangle (cutting through the length)

Yes.

Figure 9: Cylinder again
→ Slice parallel to base: Circle. ✔
→ Slice parallel to base (second box): Circle.
→ Slice perpendicular to base: Rectangle. ✔

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Row 4:

Figure 10: Triangular prism (standing on triangular base?)
Actually, this looks like a prism with triangular bases on top/bottom? No — looking at orientation, it seems like the triangular faces are vertical. Hmm.

Actually, in most textbooks, for a triangular prism, the “base” is the triangle. So:

→ Slice perpendicular to base: Cut straight down → rectangle (through the rectangular face). ✔
→ Slice parallel to base: Triangle. ✔
→ Slice parallel to base (third box): Triangle.

Wait — the labels say:

First box: “A SLICE PERPENDICULAR TO THE BASE” → should be rectangle
Second box: “A SLICE PARALLEL TO THE BASE” → triangle
Third box: “A SLICE PARALLEL TO THE BASE” → triangle

Yes.

Figure 11: Cube or rectangular prism? Looks like a cube.
→ Slice perpendicular to base: Rectangle (or square). ✔
→ Slice parallel to base: Square. ✔
→ Slice parallel to base (third box): Square.

Figure 12: Square pyramid
→ Slice perpendicular to base: Triangle. ✔
→ Slice parallel to base: Square. ✔
→ Slice perpendicular to base (third box): Triangle.

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Now, let’s list all correct answers clearly.

I’ll write them row by row, left to right.

Row 1:
1. Parallel → Square
2. Parallel → Square
3. Perpendicular → Triangle

Row 2:
4. Perpendicular → Rectangle
5. Parallel → Rectangle
6. Perpendicular → Triangle

Row 3:
7. Parallel → Circle
8. Parallel → Triangle
9. Perpendicular → Rectangle

Row 4:
10. Perpendicular → Rectangle
11. Parallel → Square
12. Perpendicular → Triangle

Wait — I think I mixed up some positions. Let me re-map based on the actual grid.

Looking back at original image layout (as described):

There are 4 rows × 3 columns = 12 figures.

Each has three boxes below it labeled:

Box A: "A SLICE PARALLEL TO THE BASE" OR "PERPENDICULAR"
Box B: same
Box C: same

And we need to color-code which shape appears.

But since we don’t have colors, we just name the shape.

Let me assign each cell properly.

Actually, better to list each figure with its three slices.

From top-left to bottom-right:

Figure 1 (Square Pyramid):
- Box 1: Parallel → Square
- Box 2: Parallel → Square
- Box 3: Perpendicular → Triangle

Figure 2 (Rectangular Prism):
- Box 1: Parallel → Rectangle
- Box 2: Parallel → Rectangle
- Box 3: Perpendicular → Rectangle

Figure 3 (Triangular Prism):
- Box 1: Parallel → Triangle
- Box 2: Parallel → Triangle
- Box 3: Perpendicular → Rectangle

Figure 4 (Cylinder):
- Box 1: Perpendicular → Rectangle
- Box 2: Parallel → Circle
- Box 3: Perpendicular → Rectangle

Figure 5 (Flat Rectangular Prism):
- Box 1: Parallel → Rectangle
- Box 2: Parallel → Rectangle
- Box 3: Perpendicular → Rectangle

Figure 6 (Square Pyramid):
- Box 1: Perpendicular → Triangle
- Box 2: Parallel → Square
- Box 3: Perpendicular → Triangle

Figure 7 (Cone):
- Box 1: Parallel → Circle
- Box 2: Parallel → Circle
- Box 3: Perpendicular → Triangle

Figure 8 (Triangular Prism - sideways):
- Box 1: Parallel → Triangle
- Box 2: Parallel → Triangle
- Box 3: Perpendicular → Rectangle

Figure 9 (Cylinder):
- Box 1: Parallel → Circle
- Box 2: Parallel → Circle
- Box 3: Perpendicular → Rectangle

Figure 10 (Triangular Prism - standing?):
Actually, looking at description, Figure 10 is a prism with triangular bases on front/back? Or top/bottom?

In many diagrams, if it's drawn with triangles on the ends, then:

- Parallel to base (triangle) → triangle
- Perpendicular → rectangle

But in the label for Figure 10, first box says “A SLICE PERPENDICULAR TO THE BASE” → so if base is triangle, perpendicular slice = rectangle

Second box: “PARALLEL” → triangle

Third box: “PARALLEL” → triangle

So:

Figure 10:
- Perpendicular → Rectangle
- Parallel → Triangle
- Parallel → Triangle

Figure 11 (Cube/Prism):
- Perpendicular → Square (or rectangle)
- Parallel → Square
- Parallel → Square

Assuming it’s a cube, all are squares.

Figure 12 (Square Pyramid):
- Perpendicular → Triangle
- Parallel → Square
- Perpendicular → Triangle

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Now, to present final answer clearly.

Since the task is to “color four colors for your key”, but we don’t have colors, we’ll just state the shape for each box.

But perhaps the expected answer is to list the shape for each of the 12 figures’ three slices.

Alternatively, maybe they want us to match the cross-section shapes.

But since the instruction is to solve the problem, and the problem is to determine what the cross section is for each case, I’ll provide the shape for each box.

To make it clean, I’ll list them in order:

For each of the 12 figures, give the three cross sections in order (left to right box).

Final Answer:

Figure 1: Square, Square, Triangle
Figure 2: Rectangle, Rectangle, Rectangle
Figure 3: Triangle, Triangle, Rectangle
Figure 4: Rectangle, Circle, Rectangle
Figure 5: Rectangle, Rectangle, Rectangle
Figure 6: Triangle, Square, Triangle
Figure 7: Circle, Circle, Triangle
Figure 8: Triangle, Triangle, Rectangle
Figure 9: Circle, Circle, Rectangle
Figure 10: Rectangle, Triangle, Triangle
Figure 11: Square, Square, Square
Figure 12: Triangle, Square, Triangle

This covers all 12 figures with their three respective cross sections.