Circles and Squares
In the activity below, a square is drawn.
The green circle just encloses the square, passing through the four corners.
The blue circle just fits inside the square.
What is the ratio of the area of the green circle to the square?
What is the ratio of the area of the blue circle to the square?
What is the ratio of the area of the green circle to the blue circle?
What happens if you change the size of the square by moving the orange points?
Can you prove your results?
The green circle just encloses the square, passing through the four corners.
The blue circle just fits inside the square.
What is the ratio of the area of the green circle to the square?
What is the ratio of the area of the blue circle to the square?
What is the ratio of the area of the green circle to the blue circle?
What happens if you change the size of the square by moving the orange points?
Can you prove your results?
Ideas for Teachers
This activity is an excellent cross between area and ratios. Start this activity by measuring and comparing areas of the shapes. Then change the square, and calculate all the areas again. Ask students to generalise their results, and then prove these using algebra.
This activity is an excellent cross between area and ratios. Start this activity by measuring and comparing areas of the shapes. Then change the square, and calculate all the areas again. Ask students to generalise their results, and then prove these using algebra.
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