Monday Maths: Vicki Robinson, Communications Officer

# #MondayMaths and polygon perimeters

Posted: 17/10/16

**We’re shaking up shapes for our #MondayMaths puzzle this week, by asking you to crack the mystery of an irregular polygon, H. **

Its perimeter is almost completely constructed from the sides of several regular polygons. The task at hand: how do we work out the missing side of *H*?

This pretty puzzling problem fits well into the end of this term’s Year 7 mastery curriculum, where students will be looking at perimeter and word problems, having previously focussed on addition and subtraction of decimals.

**Filling in the gaps**** **

- We know one side length and the total perimeter. We therefore know that we will be adding decimal numbers as we work around H’s perimeter, before subtracting from the total perimeter. This task is therefore a consolidation of our decimal addition and subtraction skills.
- Of course, we only know the side-length of the square
*A*and therefore calculating the lengths of the other regular polygons early on by using the fact that the side length of A is three times that of B would be a good strategy. This is therefore also a lovely introduction to multiplying and dividing decimals, a unit that comes up next term in Year 7 Autumn 2. - Some students may even start to see the side lengths of the polygons as simple ratios of each other, starting with
*A:B.*

**Too tricky for your year group?**

This problem consolidates everything covered throughout Year 7 Autumn 1, but can be easily modified for other year groups.

Why not restructure the problem to give the shapes non-decimal side lengths?

This would make this problem accessible to Year 5 and Year 6 students as a multi-step perimeter problem and it builds on their knowledge of regular shapes.

**Extending this task**

Ask your students how they can use all of the shapes from A to E to create the smallest and largest perimeters.

**The answer will be up on ****Twitter**** this Thursday. Get involved and share your feedback – did your class like this puzzle?**