Projections, Plans and Elevations

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Projections

This topic is all about understanding 2D projections of 3D objects. Specifically, there are 3 projections of a 3D that we will consider:

• The plan – what the shape looks like from above
• The side elevation – what the shape looks like from the side
• The front elevation – what the shape looks like from the front.

Make sure you are happy with the following before continuing:

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Plans and Elevations of a 3D Shape

Take a look at the square-based pyramid shown.

Plan

The plan is the view from above. This would show a square with one line going from each corner to the centre.

Side Elevation

If we look from the side, it would look like a triangle.

Front Elevation

This is the view you would see directly from the front. If you imagine standing in front of the pyramid and looking at it, it would look like a triangle.

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Example 1: Drawing Plans and Elevations

Draw a plan, a front elevation, and a side elevation of the 3D shape below.

This is a typical example of a shape you would be given in a question on this topic – one made of a series of $1$ cm blocks. It allows us to clearly get the dimensions of our projections right.

Plan

This would show an L-shape very clearly – $3$ blocks long and $2$ blocks wide (at the base of the L).

Side elevation

This would just show the base of the L – $2$ side-by-side $1$ cm blocks.

Front elevation

This would show the front of the L – $3$ side-by-side $1$ cm blocks.

So, the resulting $3$ projections look like:

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Example 2: Interpreting Plans and Elevations

Use the plan, front elevation and side elevation shown below to construct a drawing of the 3D shape described.

To do this, we’ll think about each projection one-by-one and consider what it means.

Plan – Shows the general shape of the object (a P shape, sort of).

Side elevation – We can see that only the third square has two levels

Front elevation –  From this we can see that only the left side has two levels.

From this we can draw the following 3D shape.

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Projections, Plans and Elevations Example Questions

As we can see, the shape is one block high and is the shape of a cross, or letter x. As a result, the plan is going to be the shape of a cross, and both elevations will only be one block high. Furthermore, we can see that in looking at both from the front and from the side, the shape in question is 3 blocks wide, so the resulting elevations will both be 3 blocks wide and 1 block high. All 3 projections are shown below.

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Firstly, looking at the plan we can see that the shape is 1 block wide, and 4 blocks long. Then, from the front elevation we can see that the shape is 2 blocks high, but at both ends the shape doesn’t actually touch the floor – those two end blocks are only attached to the top row. In this particular case, we actually don’t need the side elevation to complete the picture, the first two are enough. So, the resulting 3D shape looks like:

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The plan should show the shape from directly above. From this viewpoint it will be three units across (assuming the small square is 1 unit) hence it will look like:

The side elevation will view the shape as 3 units high:

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The plan should show the shape from directly above. From this viewpoint it will be three units (assuming the small square is 1 unit) across hence will look like:

The side elevation will view the shape as 2 units high:

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All 3 projections are as seen below.

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Projections, Plans and Elevations Worksheet and Example Questions

(NEW) Projections, Plans & Elevations Exam Style Questions - MME

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