Drawing a solid on the isometric grid
3 min 18 sThe same lesson as in Primary 5
Drawing a solid on the isometric grid
Primary 4 Nets study guide: the whole chapter, step by step
About this subtopic
The idea in brief. A cuboid on isometric paper is a solid seen from one corner. It starts at the lowest vertex, three edges leave that vertex along the paper's own three directions, what you count along an edge is the steps between the dots and never the dots themselves, and the three edges that meet at the corner at the back are dashed because no face you can see touches that corner.
Lesson video, with the working
Practice questions with worked solutions
Question 1 is free to try. The other 7 open in the free trial, each with its full working.
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7 more questions, each with its full working.Answers checked, progress kept, wrong ones come back in revision. No card needed.
Start the 7-day free trialQuestion 1 of 8 · Basic · free to tryThe cuboid below has its three edge lengths marked on it. Copy the cuboid on…The cuboid below has its three…
The cuboid below has its three edge lengths marked on it. Copy the cuboid on to the isometric grid. Every step from one dot to the next dot is 1 unit, and the hidden edges are drawn with dashes.
Work it out on paper, then open the working and check your answer against it.
Show the working and the answer
Working
- Start at the lowest vertex.
- Count 3 steps for the length, 1 step for the breadth and 5 steps up for the height, reading each one off the edge it is written on. The far end of each of those 3 edges is a vertex next to the lowest one.
- Complete the solid: 6 more edges, and each one is parallel to an edge already drawn.
- Draw the 3 edges that meet at the back-bottom corner with dashes, because they are behind the solid.
Answer: See figure: a cuboid 3 units by 1 unit by 5 units drawn from one lowest vertex, with the three edges that meet at the back-bottom corner dashed and the other nine solid.
For parents
How can I help my child understand isometric drawing?
An isometric grid helps your child show a three-dimensional object on a flat page.
What your child learns here
An isometric grid helps your child show a three-dimensional object on a flat page. The Primary 4 syllabus includes drawing representations of cubes, cuboids, prisms and pyramids. On this page, the grid gives a structure for placing edges and vertices, while the properties of the requested solid decide how those parts must join and which distances need to match.
- Read the required solid and its dimensions before choosing the grid directions needed to represent its edges.
- Count equal grid intervals along the appropriate direction for cube or cuboid edges, rather than counting only the printed dots.
- Keep corresponding parallel edges consistent so the drawing represents the intended solid instead of an unrelated collection of faces.
- Use a given number of unit cubes and information about equal layers or the base to find missing edge counts before drawing.
Does the answer make sense?
In an isometric cuboid drawing, edges representing the same dimension should follow the same grid direction and span equal numbers of intervals. Your child can compare a visible pair of corresponding edges; a different count means the drawing does not consistently represent that one length.
How to practise these questions
Basic questions ask your child to copy a labelled cuboid or draw a cube or cuboid from stated edge lengths, including hidden edges. Intermediate questions give a total number of unit cubes and information about the base or height, so the remaining dimension needs finding first. Challenge tasks use a square base or different whole-number edge lengths to determine a cuboid, or ask your child to copy a triangular prism with its hidden edges. Separate that counting work from the construction: establish the edge counts, then transfer them to the grid. Compare the finished drawing with the solution for matching dimensions, joined vertices and the requested dashed hidden edges. These tasks use cube arrangements to support the drawing; the required final response is the represented solid.
Questions parents ask
Why do square faces look slanted in an isometric drawing? The page is representing a view of the solid, rather than showing every face straight on. A square face can therefore appear as a slanted four-sided shape while still belonging to a cube. Your child should follow the drawing convention and the solid's properties, instead of trying to make every visible corner a right angle on the paper.
Is an isometric grid the same as ordinary square paper? No. Its regularly spaced points support three main drawing directions used to show depth as well as height and length. Ordinary square paper mainly supports horizontal and vertical counting. Your child should follow the grid supplied in the question and count intervals along the relevant direction, keeping the scale consistent across matching edges.
Does my child need to find dimensions before drawing? Some questions give the edge lengths directly, while others provide a number of unit cubes and conditions about the layers or base. Your child then needs to work out the missing edge counts before drawing. Dividing the total cubes into equal layers and arranging a layer in rows connects that counting information to the dimensions of the requested cuboid.