Area of Compound Shapes

To find the area of compound shapes students need to understand what the word compound means.  Therefore, I ask students to discuss in pairs a definition for the word compound and to extend it to include the shapes below.  As a result of their learning in science students agree that a compound can be defined as a mixture of elements.  In the context of today’s lesson, it is one shape formed by a mixture of rectangles.

Area of Composite Shapes

Area of Compound Shapes

I present the shapes on the board to the class and ask them to consider different mixtures of rectangles that will create the pink compound shape.

Area of Composite Shapes
Area of Composite Shapes
Area of Composite Shapes

All the students showed they could create the pink composite shape by adding two smaller rectangles together.  However, the majority of the class were unable to create it as the difference of two rectangles.

It was pleasing, that all students made a clear attempt to split the composite shape up into rectangles.   Examiner reports often explain candidates who do split up the composite shapes are far more likely to arrive at the correct solution.

As we move on to question B I ask students to calculate the composite area using the three methods we discussed and to circle the method they find easiest.  Most students prefer to add the two rectangles together rather than find the difference of them.

I ask the class to attempt question C using their preferred method.  Students who finish early are to choose a different method to check their solution.  I am pleased that about half the class chose to calculate the green area as a sum of two rectangles and the other half choosing to find it as the difference.

At this point students work independently through questions on the third slide using which ever method they prefer.  If they run into a problem, I encourage them to consider a second approach before they ask for help. 

Area of Compound Shapes Plenary

Area of Composite Shapes

The plenary takes about 12 minutes.  When I present the problem I encourage students to think carefully about the individual rectangles that make up the shape.

After a few minutes it is clear some students are struggling to progress.  For these students I take a few minutes to discuss how the blue region is formed, as shown below.

Area of Composite Shapes

The next level of support, for students who need it, includes breaking the middle shape down into individual rectangles and their dimensions.

Area of Composite Shapes

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About Mr Mathematics

My name is Jonathan Robinson and I passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.


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