Circle Area Problem
What is the area of the region bounded by the two quarter circles within this square?
How could you go about solving this problem?
How could you go about solving this problem?
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Ideas for Teachers
This is a good investigation for higher ability students, using their knowledge of areas to help them attack this seemingly very difficult problem. Show the problem on the board to the whole class, and get them to discuss in pairs how they might go about tackling this problem (it is certainly not trivial).
Once they have had a little time to think, show them the steps as hints towards a way to break this problem up. They should be able to calculate the area by step 3, but as an extension ask them to generalise the result for any square.
This is a good investigation for higher ability students, using their knowledge of areas to help them attack this seemingly very difficult problem. Show the problem on the board to the whole class, and get them to discuss in pairs how they might go about tackling this problem (it is certainly not trivial).
Once they have had a little time to think, show them the steps as hints towards a way to break this problem up. They should be able to calculate the area by step 3, but as an extension ask them to generalise the result for any square.
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