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GCSE Maths Geometry and Measure

Plans and Elevations

Plans and Elevations

Here we will learn about plans and elevations, including what they are, how to construct them and how to interpret plans and elevations to generate a 3 D image.

There are also plans and elevations worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are plans and elevations?

Plans and elevations are a way of representing a 3 -dimensional object.

We have three views of the 3 D shape:

  • From the front of the shape, called the front elevation
  • From the side of the shape, called side elevation
  • From above looking down on the shape, called the plan view

Plans and Elevations Image 1

Front elevation
 
Plans and Elevations Image 2

Side elevation
 
Plans and Elevations Image 3

Plan view
 
Plans and Elevations Image 4

What are plans and elevations?

What are plans and elevations?

How to construct plans and elevations

In order to construct plans and elevations:

  1. Draw the plan view.
  2. Draw the front elevation.
  3. Draw the side elevation.

How to construct plans and elevations

How to construct plans and elevations

Plans and elevations worksheet

Plans and elevations worksheet

Plans and elevations worksheet

Get your free plans and elevations worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Plans and elevations worksheet

Plans and elevations worksheet

Plans and elevations worksheet

Get your free plans and elevations worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Plans and elevations examples

Example 1: simple object made from cubes

Draw the three types of elevation for this object.

Plans and Elevations Example 1

  1. Draw the plan view.

Imagine you are above the shape and looking straight down.  

We would see two yellow squares next to each other, even though the cubes are different heights.

Plans and Elevations Example 1 Step 1

2Draw the front elevation.

Imagine you are in front of the shape and looking straight at it. We would see a red ‘L’ shape.

Plans and Elevations Example 1 Step 2

3Draw the side elevation.

Imagine you are at the side of the shape and looking straight at it. We would see 2 blue squares making a rectangle, even though the cubes are at different distances.

Plans and Elevations Example 1 Step 3

Solution:

Plan view
 
Plans and Elevations Example 1 Step 1

Front elevation
 
Plans and Elevations Example 1 Step 2

Side elevation
 
Plans and Elevations Example 1 Step 3

Example 2: simple shapes made from cubes

Draw the three types of elevation for this object.

Plans and Elevations Example 2

Imagine you are above the shape and looking straight down. 


We would see two yellow squares next to each other, even though the cubes are at different heights.


Plans and Elevations Example 2 Step 1

Imagine you are in front of the shape and looking straight at it. 


We would see a red ‘L’ shape.


Plans and Elevations Example 2 Step 2

Imagine you are at the side of the shape and looking straight at it.


We would see 3 blue squares making a rectangle.


Plans and Elevations Example 2 Step 3


Solution:


Plan view
 
Plans and Elevations Example 2 Step 1

Front elevation
 
Plans and Elevations Example 2 Step 2

Side elevation
 
Plans and Elevations Example 2 Step 3

Example 3: cuboid

Draw the three types of elevation for this cuboid.

Plans and Elevations Example 3

Imagine you are above the shape and looking straight down. We would see a yellow rectangle that is 3 squares wide, and 4 squares in length.


Plans and Elevations Example 3 Step 1

Imagine you are in front of the shape and looking straight at it. We would see a 2 by 3 red rectangle.


Plans and Elevations Example 3 Step 2

Imagine you are at the side of the shape and looking straight at it. We would see a 2 by 4 blue rectangle.


Plans and Elevations Example 3 Step 3


Solution:


Plan view
 
Plans and Elevations Example 3 Step 1

Front elevation
 
Plans and Elevations Example 3 Step 2

Side elevation
 
Plans and Elevations Example 3 Step 3

Step-by-step guide: Cuboid

Using plans to construct the 3D object

You need to be able to visualise the 3 D object using plans and elevations.

It is useful to recognise features within the 2 D drawings such as:

  • single squares,
  • the number of squares in a row,
  • capital letter shapes (L, T, C shapes)

Below are a few examples using these features. Note, they are not the plans and elevations of the same object.

plans and elevations new image 1plans and elevations new image 2plans and elevations new image 3plans and elevations new image 4
This plan looks like a capital L.This plan has a random square that is not in line with the other squares.This plan looks like a C shapeThis plan has 4 squares in a row.

Remember that these plans and elevations may not be flat surfaces. These two 3 D shapes below have the same plan view, but they are not the same 3 D object.

plans and elevations new image 5

Top tip: To determine the 3 D object from the plans, you must use all three plans and elevations.

How to construct the 3D object using the plans

In order to construct the 3 D object from the three elevations:

  1. Inspect the plan view.
  2. Inspect the front elevation.
  3. Inspect the side elevation.
  4. Draw the \bf{3} D object.

Constructing a 3D object examples

Example 4: constructing a simple 3D object 

A 3 D object is made from 4 identical cubes. Construct the 3 D object using the three elevations of the object given below.

Plan view
 
plans and elevations example 4.1

Front elevation
 
plans and elevations example 4.2

Side elevation
 
plans and elevations example 4.3

The plan view has three yellow squares in a row, with one square on the right hand side of the middle square.

The front elevation is two squares wide. This means that the 3 D image is only one cube high.

The side elevation is three squares wide. The middle square must not be in line with the other two squares as the front view shows the 3 D object being two squares wide, and the plan view shows that it is the middle square that is not in line.

plans and elevations example 4 step 4

Example 5: more cubes

Below are the plans and elevations of a 3 D object. Given that the object is made up of 6 congruent cubes, construct an isometric drawing of the 3 D object.

Plan view
 
plans and elevations example 5.1

Front elevation
 
plans and elevations example 5.2

Side elevation
 
plans and elevations example 5.3

The plan view has three yellow squares in a row, with one square on the right hand side of the bottom square.

The front elevation is two squares wide and 3 squares high (the same as the plan view). This means that the 3 D object must be 3 cubes high, 3 cubes deep, and 2 cubes wide.

The side elevation confirms that the shape is 3 cubes high and 3 cubes deep. From the front elevation and plan view, the square in the bottom left hand corner must not be in line with the other squares.

plans and elevations example 5 step 4

Example 6: alcoves

The following plans and elevations represent a 3 D object consisting of 10 identical cubes. Construct the 3 D object using isometric paper.

Plan view
 
plans and elevations example 6.1

Front elevation
 
plans and elevations example 6.2

Side elevation
 
plans and elevations example 6.3

The plan view consists of four yellow squares in a 2 \times 2 grid. We cannot yet determine if these squares are on the same surface.

The front elevation is 3 squares high and 2 squares wide. Given that the plan view is a 2 \times 2 grid, at least one row of two squares must not be in line with the others.

The side elevation looks like a capital C. This means that we have an alcove (a recess) in the centre of the front elevation.


The top and bottom rows of the front elevation must be in line with each other, but not with the middle row.

plans and elevations example 6 step 4

Common misconceptions

  • Elevations

The front elevation and the side elevation can be labelled the other way around. If the diagram has one arrow – then this is the front elevation.

Plans and Elevations Common Misconceptions Image 1

  • \bf{3} D cubes and cuboids

A 2 D drawing of a cube using isometric paper uses 60^o and 120^o angles. But the cube has 90^o angles, as do the plans and elevations. A large proportion of plans and elevations are based on squares and rectangles.

  • Rectangles are acceptable in place of individual squares

If you are drawing the plan and elevation of a cuboid, it is acceptable to draw rectangles to show the sides with the correct dimensions, rather than lots of individual squares. For example,

Plans and Elevations Common Misconceptions Image 2

Plans and Elevations Common Misconceptions Image 3

Practice plans and elevations questions

1. The following object is a cuboid with the dimensions 2cm \times 3cm \times 6cm. The cuboid is made from 36 identical cubes. Which diagram shows the plan view of the 3 D object? The front elevation (F) has been labelled.

 

plans and elevations practice question 1 NEW

plans and elevations practice question 1a NEW

GCSE Quiz False

plans and elevations practice question 1B new

GCSE Quiz True

plans and elevations practice question 1c new

GCSE Quiz False

plans and elevations practice question 1D new

GCSE Quiz False

The plan view is overhead. We can see that it is a rectangle that is 2 squares wide and 6 squares in length.

 

plans and elevations practice question 1B new

2. The 3 D object below is made from 10 identical cubes. Which of the following is the side elevation of the 3 D object?

 

plans and elevations practice question 2 new

plans and elevations practice question 2a new

GCSE Quiz False

plans and elevations practice question 2b new

GCSE Quiz False

plans and elevations practice question 2c new

GCSE Quiz False

plans and elevations practice question 2d new

GCSE Quiz True

As the front elevation is looking at the object from the left for this question, the side elevation will be made from looking at the object from the right. We would see 4 blue squares making a vertical line, then add the additional two squares at the left of the drawing from the second row.

 

plans and elevations practice question 2d new

3. The following 3 D object is constructed using 7 identical cubes. Construct the side elevation of the object.

 

plans and elevations practice question 3 new

plans and elevations practice question 3a new

GCSE Quiz False

plans and elevations practice question 3b new

GCSE Quiz False

plans and elevations practice question 3c new

GCSE Quiz False

plans and elevations practice question 3d new

GCSE Quiz True

From the side view, we can see three squares in line, with one square to the left on the bottom row.

 

plans and elevations practice question 3d new

4. Which of the objects below has the following plan view, front elevation, and side elevation.?

 

Plan view Front elevation Side elevation
Plans and Elevations Practice Question 4 Image 1 Plans and Elevations Practice Question 4 Image 2 Plans and Elevations Practice Question 4 Image 3

 

Plans and Elevations Practice Question 4 Image 1a

GCSE Quiz True

Plans and Elevations Practice Question 4 Image 4-2

GCSE Quiz False

Plans and Elevations Practice Question 4 Image 4 - 3

GCSE Quiz False

Plans and Elevations Practice Question 4 Image 4 - 4

GCSE Quiz False

The plan view is a 2 \times 3 rectangle, the front elevation is a 3 \times 2 rectangle, and the side elevation is a 3 \times 3 square.

 

Plans and Elevations Practice Question 4 Explanation Image

5. Which of the objects corresponds to the plan and elevations?

 

Plan view Front elevation Side elevation
Plans and Elevations Example 5 Step 1 Plans and Elevations Example 5 Step 2 Plans and Elevations Example 5 Step 3

 

Plans and Elevations Practice Question 4 Image 4

GCSE Quiz True

Plans and Elevations Practice Question 4 Image 5

GCSE Quiz False

Plans and Elevations Practice Question 4 Image 6

GCSE Quiz False

Plans and Elevations Practice Question 4 Image 7

GCSE Quiz False

The plan view is a 2\times 5 rectangle. The front view is a 2 \times 3 rectangle, and the side view is a 5 \times 3 rectangle.

 

Plans and Elevations Practice Question 5 Explanation Image

6. Which of the objects corresponds to the plan and elevations?

 

Plan view Front elevation Side elevation
Plans and Elevations Practice Question 6 Image 1 Plans and Elevations Practice Question 6 Image 2 Plans and Elevations Practice Question 6 Image 3

Plans and Elevations Practice Question 6 Image 5

GCSE Quiz False

Plans and Elevations Practice Question 6 Image 2.2

GCSE Quiz False

Plans and Elevations Practice Question 6 Image 6

GCSE Quiz False

Plans and Elevations Practice Question 6 Image 4

GCSE Quiz True

The object is mostly only one cube high, with only one additional cube of the second layer, in the middle column.

 

Plans and Elevations Practice Question 6 Explanation Image

 

 

Plans and elevations GCSE questions

1. The plan view, front elevation and side elevation of a solid are shown.

 

Plans and Elevations GCSE Question 1 Image 1

 

Which of these solids corresponds to the views?

Cuboid      Cylinder      Cone      Sphere

 

(1 mark)

Show answer

Plans and Elevations GCSE Question 1 Image 2

Cylinder

(1)

2. The plan view, front elevation and side elevation of a solid are shown.

 

Plan view Front elevation Side elevation
Plans and Elevations GCSE Question 2 Image 1 Plans and Elevations GCSE Question 2 Image 2 Plans and Elevations GCSE Question 2 Image 3

How many cubes are used to make the solid?

 

8 \text{ cubes} \quad \quad 10 \text{ cubes} \quad \quad 12 \text{ cubes} \quad \quad 14 \text{ cubes}

(1 mark)

Show answer

 

Plans and Elevations GCSE Question 2 Image 4

8 \text{ cubes}

(1)

3. The diagram shows a cuboid.

 

Plans and Elevations GCSE Question 3 Image 1

 

On the centimeter grid below draw accurately the plan of the cuboid.

 

Plans and Elevations GCSE Question 3 Image 2

 

(2 marks)

Show answer

 

Plans and Elevations GCSE Question 3 Image 3

 

For a rectangle

(1)

For the correct rectangle – 7 \ cm by 2 \ cm

(1)

4. The diagram shows a prism with a cross section in the shape of a pentagon.

 

Plans and Elevations GCSE Question 4 Image 1

 

On the centimetre grid below draw the front elevation and the side elevation.

 

Plans and Elevations GCSE Question 4 Image 2

 

(4 marks)

Show answer

Plans and Elevations GCSE Question 4 Image 3

 

For the front elevation – square 3 by 3

(1)

For the front elevation – line across, splitting into 2 rectangles

(1)

 

For the side elevation – a pentagon with base 3 and height 3

(1)

For side elevation – correct pentagon

(1)

Learning checklist

You have now learned how to:

  • Construct plans and elevations
  • Interpret plans and elevations

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