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Shapes in Space

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Shapes in Space

You are helping plan a pop-up gallery of geometric sculptures. Use the diagrams and clues to classify shapes, check properties and solve the design challenges. Show working where useful.

Gallery shape files

Use the labelled shape cards to answer Questions 1–3.

A CUBE 6 square faces

B TRIANGULAR PRISM 2 triangular faces 3 rectangular faces

C SQUARE-BASED PYRAMID 1 square base 4 triangular faces

1.Which sculpture card shows a polyhedron with exactly 5 faces, 4 of which are triangles? Name it and state how many of its faces are triangles.

2.A visitor says, “Every face of a triangular prism is a triangle.” Use Card B to correct the visitor with the face shapes and their counts.

3.Which card represents a solid with 8 vertices and 12 edges? Explain briefly how you know.

Build and classify

Think like a designer: connect flat shapes to solid forms, then test a rule.

4.A sculpture is made from 2 identical triangular ends joined by 3 rectangles. What 3D shape is it? How many faces, edges and vertices does it have?

5.Match each solid to the 2D shapes used for its faces. Write the correct letter beside each number.

1. Cube
2. Triangular prism
3. Square-based pyramid

B. Six squares
A. Two triangles and three rectangles
C. One square and four triangles

6.A classmate argues that a rectangle is always a regular polygon because all its angles are equal. Is the argument correct? Explain using the definition of a regular polygon.

7.Select all the regular polygons in this set: an equilateral triangle, a non-square rectangle, a square and an irregular pentagon.

Equilateral triangle
Non-square rectangle
Square
Irregular pentagon

Net-work and design challenge

Use geometric reasoning to help the gallery team finish its plans.

8.Draw one possible net for a cube. Your net must use six equal squares joined edge-to-edge and must fold into a cube without overlap.

9.The gallery needs a solid with 6 faces, 12 edges and 8 vertices. Name one possible solid and explain how its faces could be arranged.

10.In a polyhedron, each edge belongs to two faces. A solid has 5 faces, and the total number of face-edges counted across all faces is 18. How many edges does the solid have? Show the calculation.

11.Sketch an irregular quadrilateral for a gallery floor tile. Label its four sides and explain one property that makes it irregular.

12.A student sorts solids into two groups: Group X has only flat polygon faces; Group Y includes at least one curved surface. Give one example for each group and state which group contains a cylinder.