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3D Geometry Project

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3D Geometry Project

A coastal community needs a lightweight shelter made from flat panels. Use your 3D geometry knowledge to plan a model, test its net and explain why its shape works. Show your calculations and include units where needed.

Choose and analyse a shelter shape

Use the shape reference cards below. A face is a flat surface; an edge is where two faces meet; a vertex is a corner.

Triangular prism: 5 faces, 9 edges, 6 vertices

Square-based pyramid: 5 faces, 8 edges, 5 vertices

Rectangular prism: 6 faces, 12 edges, 8 vertices

1.Which reference shape would make the most practical shelter if the panels need to be cut from flat material and the roof should slope? Choose one and give a geometrical reason.

2.A triangular-prism shelter has two triangular ends and three rectangular side faces. How many faces, edges and vertices does it have altogether? Check your totals against the reference card.

3.True or false? A triangular prism is a pyramid because it has triangular faces. Explain the feature that distinguishes a prism from a pyramid.

Plan the panels

The design team is testing a triangular-prism shelter with a length of 2.4 m. Each triangular end has a base of 1.8 m and a perpendicular height of 1.2 m. Each sloping side of the triangle is 1.5 m.

4.Calculate the area of one triangular end. Use the perpendicular height, not a sloping side.

5.The two triangular ends are made from separate panels. What total area of material is needed for both ends, before allowing for tabs or waste?

6.Find the area of all three rectangular side panels. The rectangles have widths 1.8 m, 1.5 m and 1.5 m, and each is 2.4 m long. Give the combined area.

7.Work out the total surface area of the closed triangular prism, including both triangular ends and all three rectangular faces.

8.A supplier sells panel material in sheets of 5 m². How many whole sheets should the team buy to cover 13.68 m²? State why rounding down is not suitable.

Create and explain a net

Use the drawing space to sketch a net for the shelter’s triangular-prism shape. Include two matching triangular ends and three rectangles. Label the rectangle lengths and widths using the measurements above; show where the triangles attach.

Check that each of the three triangle sides matches one rectangle width. Add tabs only if you want to show how the model could be joined.

9.Explain how your flat net folds to make a triangular prism. Refer to the matching edges and the two triangular ends.

10.The shelter needs a waterproof cover over its two sloping roof panels only. Each roof panel is 2.4 m long and 1.5 m wide. What cover area is needed, before allowing for overlap?