Polygons part 2 in #MondayMaths

Monday Maths: Vicki Robinson, Communications Officer

Polygons part 2 in #MondayMaths

Posted: 24/10/16

Following on from last week’s theme of irregular polygons and perimeters, this week’s #MondayMaths tackles a selection of even stranger shapes with some trusted squared paper.

It’s half term now, so we’ll all be moving into Autumn 2 next week. Our Year 7 mastery students will be looking at calculating areas of rectangles and triangles. On the strength of that skill and knowledge, this puzzle challenges their ability to recognise composite shapes and create strategies for calculating their areas.

Starting from the basics

As we can see, all the shapes above are built on combinations of rectangles and triangles, including the subtraction of triangles and rectangles.

Here’s an example showing how this shape can be visualised as a triangle subtracted from a rectangle to create a new irregular polygon:

rectangle with triangle cut out

Can you explain why?

This problem is a great opportunity for students to explore geometric calculation strategies and explain their decisions using correct mathematical language.

*Note the question asks students to sort the shapes into groups with the same area, so once a student has found the area of one shape, it might be worth trying to immediately hypothesise which of the other shapes share that area.

Remember to encourage students to explain their reasoning, and to check their hypothesis through calculation.

Extending the exercise

  • You could ask students to construct as many different shapes of the same area as they can, explaining how they know the shapes have the same area.
  • Alternatively, ask students to find composite shapes in the real world and discuss how they might calculate their areas (logos and floor plans are a good place to start).
  • Students who have studied simple 3-D shapes in Year 8 and beyond might like to try a three-dimensional version of this problem with composite cuboids and prisms.

Which polygon puzzle did you prefer – this one or last week’s? Let us know on Twitter where you can find the answer on Thursday.