Matemáticas
Plan and Elevation: Three Flat Views of One Solid
The plan looks down, the elevations look from the front and the side. One L-shaped solid drawn all three ways, with the lines students leave out.
Plan and elevation
A plan is the view of a solid from directly above; an elevation is the view from directly in front of it or directly from one side.
- También llamado
- Plan view, Orthographic projection
- Dónde lo encuentra el alumnado
- Grade 8 mathematics, and at GCSE where plans and elevations of solids built from cubes are drawn on squared paper.
La respuesta corta
A plan is the view of a solid seen from directly above. An elevation is the view seen from directly in front or directly from one side. Together the plan, front elevation and side elevation describe a three-dimensional object using three flat drawings, each drawn to scale with no perspective.
Un ejemplo
Front elevation: 4 squares wide and 3 tall, with a 2 by 2 notch cut from the top right
Take a solid 4 cm wide, 2 cm deep and 3 cm tall, with a block 2 cm wide and 2 cm tall removed from the top right so that it looks like a letter L from the front. The plan is a plain 4 by 2 rectangle, with a line across it marking the edge where the tall part ends. The front elevation is the L itself. The side elevation is a 2 by 3 rectangle with a line 1 unit up, showing the top of the lower part.
Three views, no perspective
The plan looks straight down. The front elevation looks straight at the front face. The side elevation looks straight at one side, and the question will say which side. Every view is drawn as though the eye were infinitely far away, so nothing shrinks with distance.
That is the difference between this and a sketch of a solid. In a sketch, a cube's top face is drawn as a squashed parallelogram. In a plan, the same face is a true square. A part 2 cm wide occupies 2 squares on the paper wherever it happens to sit in the solid.
One L-shaped solid, drawn three ways
Work through the example solid view by view rather than trying to picture all three at once. From above, only the outline of the footprint is visible: a 4 by 2 rectangle. From the front, the step is visible and produces the L. From the side, you see the tall block's silhouette behind the low one, so the outline is a plain rectangle 2 wide and 3 tall.
Two habits make this reliable. Count squares rather than estimating, and check that shared measurements agree between the views — the plan and the front elevation must report the same 4 cm width, and the plan and the side elevation must report the same 2 cm depth. Views that disagree cannot both be right.
The lines that get left out
Where a step or a change of height occurs, an edge is visible in the view and must be drawn as a line inside the outline. On the L-shaped solid, the plan needs a line across it where the tall part stops, and the side elevation needs one at the height of the low part. Drawing only the outer boundary loses those edges and, with them, the marks.
The usual arrangement on the page places the plan above the front elevation with the side elevation beside it, but questions ask for the views one at a time and expect each to be labelled. Labelling matters more than positioning: an unlabelled correct drawing invites the examiner to guess which view it is.
Preguntas frecuentes
What is the difference between a plan and an elevation?
A plan is the view from directly above, looking down on the solid. An elevation is a view from the side of it — the front elevation from the front, the side elevation from the left or right, whichever the question names. Together the three describe the solid fully.
Do you draw hidden edges on a plan or elevation?
Edges that are genuinely visible from that direction are drawn as solid lines, including internal ones where the surface steps up or down. Edges hidden behind the solid are not part of a standard GCSE answer. If a question asks for hidden detail it will say so, usually specifying dashed lines.
Why do the three views have to agree with each other?
Because each is a measurement of the same object. The width read from the plan must match the width read from the front elevation, and the depth from the plan must match the depth from the side elevation. Checking those two pairs catches most errors before the drawing is handed in.
Can you rebuild a solid from its three views?
Usually, but not always. The three views pin down the outline of the solid from each direction, and for the cube-built shapes used in exams that is normally enough. Some solids with hollows or hidden steps produce identical views, which is why technical drawing adds extra sections.
Última actualización
Saber la palabra no es lo mismo que usarla
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