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You will need squared paper for this activity.
Start by drawing a set of axes like this:
Then, draw the following lines:
From (1,1) to (4,5)
From (4,5) to (8,8)
From (1,1) to (5,4)
From (5,4) to (8,8)
Then measure each of the four lines accurately.
What shape have you drawn?
Now, measure the distance from the bottom left to the top right of your picture (the long diagonal of the shape).
What is the length of the short diagonal?
Pupils could create their own shapes on squared paper and pose challenges for others to measure and draw within those shapes.
Drawing
Age 5 to 11
Challenge Level 
Drawing
You will need squared paper for this activity.
Start by drawing a set of axes like this:
Then, draw the following lines:
From (1,1) to (4,5)
From (4,5) to (8,8)
From (1,1) to (5,4)
From (5,4) to (8,8)
Then measure each of the four lines accurately.
What shape have you drawn?
Now, measure the distance from the bottom left to the top right of your picture (the long diagonal of the shape).
What is the length of the short diagonal?
Why do this problem?
This problem gives pupils the opportunity to draw carefully and then measure. The measuring requires a degree of accuracy.
Possible approach
Have a discussion with the pupils about what you have to do to draw and measure lines accurately. You could then introduce the problem itself, encouraging children to use squared paper.
Key questions
How are you sure that you have done this accurately?
Possible extension
You could invite pupils to find out what happens with other rhombuses.Pupils could create their own shapes on squared paper and pose challenges for others to measure and draw within those shapes.
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