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2D and 3D Shapes
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2D and 3D Shapes
A coastal visitor centre in Aotearoa is planning a new display made from geometric solids. Use shape properties, nets and views to check the designs. Show your reasoning where asked.
Spot the shapes
Classify the shapes in the design kit, then compare their properties.
1.The kit contains a triangle, a rectangle, a hexagon, a cube, a triangular prism and a cylinder. Which three are 2D shapes?
2.A display stand is a rectangular prism. How many faces, edges and vertices does it have?
3.Which statement about a regular hexagon is correct?
- It has 5 sides and 5 vertices.
- It has 6 equal sides and 6 vertices.
- It has 6 curved sides.
- It has 8 right angles.
4.A rectangle has two pairs of parallel sides. True or false? Explain briefly.
Build and inspect
Use faces and nets to imagine how flat shapes fold into solids.
5.A triangular prism has two triangular ends and three rectangular side faces. How many faces does it have altogether?
6.Select the shapes needed for a net of a triangular prism.
- 2 triangles and 3 rectangles
- 2 squares and 4 triangles
- 1 triangle and 3 circles
- 6 rectangles
7.Draw one possible net for a cube. Your drawing should show six equal squares joined edge to edge.
8.A closed cube net has 6 faces. How many edges and vertices will the folded cube have?
Views and design decisions
Apply geometry to the visitor centre’s practical design choices.
9.A box-shaped display has a rectangular front face. Looking straight at its front, which 2D shape would you see?
10.A designer reflects a triangle across a line. Which properties stay unchanged: side lengths, angle sizes, number of sides, or position?
- Side lengths, angle sizes and number of sides
- Position only
- Angle sizes and position only
- None of them
11.Complete each statement with translation, rotation or reflection: (a) A shape slides without turning. (b) A shape turns around a fixed point. (c) A shape flips across a line.
12.A builder braces a lightweight display frame with triangular supports. Explain one reason triangles are useful in structures.
3 printable pages
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