Properties and constructions: interpret plans and elevations of 3D shapes

The idea

A plan is the view from directly above a 3D shape, and elevations are views from the front and side. To interpret them, match each 2D outline to the direction it represents: the plan shows the footprint, the front elevation shows the face seen from the front, and the side elevation shows the face seen from the side. For a cuboid 5 cm long, 3 cm wide and 2 cm high, the plan is a 5 cm by 3 cm rectangle, the front elevation is 5 cm by 2 cm, and the side elevation is 3 cm by 2 cm. Hidden edges are not drawn in these orthographic views, so use the given dimensions and the arrangement of rectangles to decide the shape. Check that every visible face is accounted for and that the views are consistent with one another.

What earns the marks

• Identify the plan as the view from directly above the shape.
• Identify the front elevation as the view from the front of the shape.
• Identify the side elevation as the view from the side of the shape.
• Match each 2D view to the correct direction and use given dimensions to deduce the 3D shape.
• Recognise that hidden edges are not shown in plans and elevations.

Common mistakes and how to put them right

• Confusing the plan with the front elevation.

  Put it right: The plan is always the view from above, not from the front.

• Assuming that a side elevation is the same as a front elevation.

  Put it right: They show different faces and may have different dimensions.

• Drawing hidden edges in a plan or elevation.

  Put it right: These views show only visible outlines, so hidden edges are omitted.

Exam tips

• Label each view clearly as plan, front elevation or side elevation before matching dimensions.
• Use the given lengths to check that the plan, front and side views are mutually consistent.
• If a view is a rectangle, consider what that tells you about the face it represents and the shape as a whole.