Paper Together: sit a paper in a room with your friends.See how it works
Plans & elevations: worked examples and method
Foundation and Higher · Grade 4 · Non-calculator
This page sets out the method for plans & elevations in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Plans & elevations topic page.
Key facts
Plan = view from directly above. Front elevation = view from the front. Side elevation = view from the side (the question says which side).
Each view is a 2D drawing — no perspective, no slanted lines for depth.
The width of the front elevation matches the width of the plan; the height of the front and side elevations match each other.
A line inside a view shows an edge where two faces meet at different depths.
A cylinder standing up: plan is a circle, elevations are rectangles. A cone on its base: plan is a circle (with a dot), elevations are triangles.
From cubes: the plan shows which floor squares are covered, and each elevation shows the tallest column in each row.
The method, step by step
Method: draw the three views of a cube solid
When a solid made from centimetre cubes is shown and you must draw the plan and elevations.
Plan: look straight down. Shade a square for every column of cubes, whatever its height.
Front elevation: for each column left to right, draw a stack as tall as the tallest cube in that line of sight.
Side elevation: repeat from the side shown by the arrow, again using the tallest cube in each line.
Add internal lines wherever the height changes.
Check the widths and heights of the three views agree with each other.
Method: rebuild a solid from its views
When you are given the plan and elevations and asked how many cubes or to sketch the solid.
Use the plan to place a cube on every shaded floor square.
Use the front elevation to see how tall each column from left to right must be.
Use the side elevation to decide which of those columns is actually the tall one.
Count the cubes (or draw the solid on isometric paper).
How the lesson explains it
Three views
The plan is from above. The front elevation is from the front. The side elevation is from the side.
Each view is a flat shape, not a 3D sketch.
What you can see
Draw the outline of the faces you would see from that direction.
A height that is hidden behind a taller block does not add a new outer edge if it is completely behind.
Lengths
The plan uses the length and the width. The front elevation uses the width and the height.
Do not put the height on the plan.
A cuboid
All three views of a cuboid are rectangles.
The plan is length by width. The front is width by height. The side is length by height.
A prism
The plan of a triangular prism depends on which way the triangle points.
The elevation that faces the triangle shows the triangle. The other shows rectangles.
Scale
If the views are drawn to scale, use the scale before you read off a real length.
The view itself does not change the real size.
Plan, front and side
Stand above the solid and look down. That drawing is the plan. You see the grid of squares that have cubes on them, and you do not see how tall the stacks are. A single tower of 4 cubes has a plan that is one square. Its front elevation is a rectangle 1 by 4, because from the front you see the full height. The side elevation of that same tower is also a 1 by 4 rectangle, since a single column looks the same from the side as from the front.
Label the views. “Plan” means above, “front elevation” means the front face, and “side elevation” means a side. Do not draw the height on the plan, and do not draw the depth on the front elevation unless a cube sticks out to the side. If two cubes are one behind the other, the front elevation shows one column, and the plan shows two squares, one in front of the other.
Method: 1. Draw the plan as the footprint only, with no heights. 2. A tower of 4 cubes has a plan of 1 square. 3. Draw the front and the side each as a 1 by 4 rectangle.
Heights and hidden cubes
On an elevation, the number of squares up a column is the height of the tallest stack in that line of sight. A cube sitting behind a stack of height 2 does not add a third square to the front view. It is hidden. You only know it is there if the plan or the side elevation shows the extra depth. When you count cubes for a volume or a total, include the hidden ones.
An L-shaped arrangement is a useful check. Three cubes in a row, plus one cube on the end sitting at the back, use 3 + 1 = 4 cubes. The plan is four squares in an L. The front elevation depends on which way you call the front: if you face the row of three, you see three squares in a row of height 1, and the back cube is hidden behind the end. The plan is what proves the fourth cube is there.
Method: 1. On an elevation, draw only the tallest cube in each line of sight. 2. A cube behind a stack of height 2 stays hidden on that view. 3. Count an L as 3+1=4 cubes, and use the plan to show the hidden cube.
Making the views agree
Build the solid so that every view is possible at once. Suppose the front elevation shows three columns with heights 2, 1 and 2. That fixes three positions across the width, and it fixes the minimum number of cubes if each column is only one deep: 2 + 1 + 2 = 5. The side elevation can demand more depth. If the two tall columns are each two cubes deep, and the middle column is only one cube deep, the side view has a depth of 2, and the cubes are no longer five.
Count that solid column by column. Each tall column is height 2 and depth 2, so it holds 2 × 2 = 4 cubes. Two tall columns hold 8 cubes. The middle column is height 1 and depth 1, so it holds 1 cube. The total is 4 + 1 + 4 = 9. The front still shows 2, 1, 2, because depth does not change the front height. This is a definite solid, not a guess: the depths are part of the description, so 9 is the count.
Method: 1. Read the front heights first, then multiply each column by its depth. 2. Heights 2, 1 and 2, each one deep, use 2+1+2=5 cubes. 3. Two-deep tall columns change the count to 2× 2+1+2× 2=9.
A slab with one cube on a corner
A 3 by 2 by 1 slab is a flat layer of cubes, three one way and two the other, one cube high. The number of cubes in the layer is 3 × 2 = 6. The plan is a 3 by 2 rectangle. The front elevation is a 3 by 1 rectangle, and the side elevation is a 2 by 1 rectangle.
Put one extra cube on a corner of that slab, stacked on a cube that is already there. The cube count becomes 6 + 1 = 7, which is 3 × 2 + 1. The plan stays 3 by 2, because the extra cube sits above an existing square and does not cover a new square of floor. The front elevation grows by one square at that corner, so one column becomes height 2 and the rest stay height 1. Always check whether an added cube changes the plan or only the elevation.
Method: 1. Count a flat slab as length times width. 2. A 3 by 2 by 1 slab uses 3× 2=6 cubes. 3. One cube stacked on a corner makes 6+1=7, and the plan stays 3 by 2.
Which measurements go in which view
A solid has three standard views. The plan is the view from above and shows the length and the width. The front elevation is the view from the front and shows the length and the height. The side elevation is the view from the side and shows the width and the height. If you learn which two measurements each view uses, you can find any missing size without drawing anything.
For example, a cuboid 5 cm long, 3 cm wide and 2 cm high has a plan of 5 by 3, a front elevation of 5 by 2 and a side elevation of 3 by 2. Exam questions often turn this round and give you the area of a view and ask for a missing edge. Divide the area by the measurement you already know, and keep track of which view you are using.
Method: 1. Name the view: plan (length by width), front (length by height) or side (width by height). 2. Write the two measurements for that view. 3. Use the area or the volume to find any missing size. 4. Check that the same edge has the same length in every view that shows it.
Tip: The height appears in both the front and the side elevation, so the two views must agree on it.
Counting cubes from heights on a plan
Some questions draw the plan as a grid and write a number in each square to give the number of cubes stacked there. To count the cubes in the whole solid, add all the numbers. To find a front elevation, look at each column from left to right and take the largest number in that column, because taller stacks hide shorter ones. The side elevation works in the same way for each row.
Remember that an elevation only shows the outline. A square with height 2 behind a square with height 3 cannot be seen from the front. When a question asks for an elevation, write the heights as a list, for example 2, 3, 2, or draw the columns in that order. Check by making sure the largest number in your elevation also appears on the plan.
Method: 1. Add every number on the plan to get the total number of cubes. 2. For the front elevation, take the largest number in each column. 3. For the side elevation, take the largest number in each row. 4. Compare the tallest value in each elevation: they must be the same.
The most and fewest cubes that fit two views
Higher questions give only the front and side elevations and ask for the maximum and minimum number of cubes. For the maximum, each square in the grid can hold the smaller of the two heights shown for its column and its row, so you work out each cell as a minimum and add them. Here you fill the solid as much as the two views allow.
For the minimum, you only need to place enough cubes to create every height that is shown. Each column height in the front elevation must appear in at least one cell, and each row height in the side elevation must appear in at least one cell. Try to use a single stack to satisfy both views at once, where the heights match. Write each cell you use and add them up.
Method: 1. Draw a grid with the front columns across and the side rows down. 2. For the maximum, put the smaller of the two heights in every cell and add. 3. For the minimum, place the tallest stack in one cell, then add only the stacks still needed. 4. Check that your cell heights reproduce both elevations exactly.
Tip: If both views have a tallest value of 3, the two views are consistent. If they disagree, the solid cannot exist.
Prisms, pyramids and cylinders
For a prism, one elevation is the cross-section and another is a rectangle. A triangular prism lying with a rectangular face on the table has a triangle as one elevation, a rectangle as the plan and a rectangle as the other elevation. The volume of any prism is the area of the cross-section times the length, and you can read both of these from the views.
For a square-based pyramid, the plan is a square with the corners joined to the centre, and both elevations are triangles. The height of the triangle in an elevation is the vertical height of the pyramid, not the slant height. The slant height is longer, and you find it with Pythagoras using the vertical height and half of the base. Mixing these two heights is a regular exam error.
Method: 1. Sketch the solid and decide which face is on the table. 2. List the shape of the plan, the front elevation and the side elevation. 3. Use vertical height for elevations and slant height for sloping faces. 4. For a prism, volume is cross-section area times length.