Plans and Elevations KS3 Maths: Drawing 2D Views of 3D Shapes

Plans and elevations are two-dimensional drawings that represent a three-dimensional shape viewed from specific directions. The plan is the view from directly above; the front elevation is the view from the front; the side elevation is the view from the right (unless stated otherwise). Together, these three views contain enough information to reconstruct the solid completely.

What are the three standard views and what does each show?

View | Direction | Dimensions visible
Plan (top view) | Directly above, looking straight down | Length and depth of base
Front elevation | Directly in front, looking horizontally | Length and height
Side elevation | From the right, looking left | Depth and height

On a standard layout, the plan sits above the front elevation (aligned left), and the side elevation sits to the right of the front elevation. Heights in the front and side elevations must always agree. Widths in the plan and front elevation must always agree.

Hidden edges — edges that exist on the solid but cannot be seen from the viewing direction — are drawn as dashed lines.

How do you draw the views of a cuboid?

Worked example 1 — cuboid 5 cm × 3 cm × 4 cm (length × depth × height)

The cuboid sits on a table with the 5 cm edge running left-to-right, 3 cm front-to-back, and 4 cm vertically.

Plan (from above): A rectangle 5 cm wide and 3 cm deep.

Front elevation: A rectangle 5 cm wide and 4 cm tall.

Side elevation (from right): A rectangle 3 cm deep and 4 cm tall.

View | Dimensions
Plan | 5 × 3 cm
Front elevation | 5 × 4 cm
Side elevation | 3 × 4 cm

A plain cuboid has no hidden edges in any view.

How do you draw the views of a stepped solid?

Worked example 2 — L-shaped step solid

A solid is built from two cuboids sharing the same base:

Left cuboid: 3 cm wide, 2 cm deep, 4 cm tall

Right cuboid: 3 cm wide, 2 cm deep, 2 cm tall

Plan (from above): The plan is a single rectangle 6 cm × 2 cm. A solid line at the 3 cm mark shows the step edge.

Front elevation: The left half (3 cm wide) rises to 4 cm; the right half (3 cm wide) rises to 2 cm. The outline is a step-shape: up 4 cm, across 3 cm, down 2 cm, across 3 cm, down 2 cm.

Side elevation (from right): Only the right cuboid is visible — a rectangle 2 cm deep and 2 cm tall. The taller left cuboid's top edge appears as a dashed line at height 4 cm.

How do you reconstruct a 3D shape from its three views?

Work through each view in order:

Use the plan to establish the footprint (length and depth).

Use the front elevation to determine height at each horizontal position.

Use the side elevation to verify depth and confirm heights.

Cross-check: widths in plan = widths in front elevation; depths in plan = widths in side elevation; heights in front and side elevations must match.

What do the views look like for common 3D shapes?

3D shape | Plan | Front elevation | Side elevation
Cube | Square | Square | Square
Cuboid | Rectangle | Rectangle | Rectangle
Cylinder (upright) | Circle | Rectangle | Rectangle
Cone (upright) | Circle with centre dot | Triangle | Triangle
Square-based pyramid | Square with diagonals | Triangle | Triangle
Sphere | Circle | Circle | Circle

For a cylinder of radius 3 cm and height 6 cm, the plan is a circle of radius 3 cm, and both elevations are rectangles 6 cm wide and 6 cm tall.

What mistakes do students most often make?

Mistake 1 — Confusing perspective sketches with elevations.
Elevations are flat projections, not 3D perspective drawings. Draw rectangles and straight lines on a square grid.

Mistake 2 — Omitting dashed lines for hidden edges.
After drawing each view, ask: "Are there edges I know exist but cannot see?" If yes, add dashed lines.

Mistake 3 — Heights not matching between views.
The maximum height in the front elevation must equal the maximum height in the side elevation.

Mistake 4 — Not labelling views.
Label each drawing: Plan, Front Elevation, Side Elevation. Examiners need to know which is which.

Frequently asked questions

Which direction is the side elevation taken from?

The standard UK convention is from the right of the shape (looking left), unless the question states otherwise. Some questions specify left or provide an arrow — always follow the instruction given. If only "side elevation" is stated, use the right side.

When should I use dashed lines?

Use dashed lines for hidden edges — edges that exist on the solid but lie behind it when viewed from that direction. If you can trace a straight line from the edge to your eye without passing through the solid, the edge is visible (solid line). If the line must pass through the solid, the edge is hidden (dashed line).

How do plans and elevations relate to real life?

Plans and elevations are the standard language of architecture and engineering. A building's floor plan is its plan view; the facade drawing is the front elevation. Engineers use orthographic projection — essentially plans and elevations — to specify components for manufacture. Understanding this link helps you see why the skill matters beyond the classroom.

Can one view be sufficient to describe a shape?

No — a single view loses information about the third dimension. A square plan is consistent with a cube, a tall cuboid, a pyramid, or a cylinder. It typically takes all three views to specify a shape without ambiguity. This is why the three standard views are always drawn together.

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