1. Four Crescents What’s the area of the four yellow crescents?

2. Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents?

3. Compare your answers with others – What do you notice? – Can you justify any inferences you make? Try the problem with different rectangle dimensions, e.g. 5cm x 4cm, 16cm x 7cm, anything you like – What do you notice now? Can you prove your assertions? Four Crescents

4. Let’s look at the general case.

5. = -

6. = = = =

7. = - = - =

8. = So, the area of the four crescents is the same as the area of the rectangle! Go back and check your earlier results.

9. Final thought

10. Resources Surds

11. SIC_8

27. Resources 900

31. Originals

32. 450 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 2 cm NOT to scale SIC_8

33. 300 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 3 cm NOT to scale SIC_8

34. 225 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 4 cm NOT to scale SIC_8

35. 150 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 6 cm NOT to scale SIC_8

36. 100 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 9 cm NOT to scale SIC_8

37. 60 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 15 cm NOT to scale SIC_8

38. 50 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 18 cm NOT to scale SIC_8

39. 36 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 25 cm NOT to scale SIC_8

40. 75 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 12 cm NOT to scale SIC_8

41. 180 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 5 cm NOT to scale SIC_8

42. 45 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 20 cm NOT to scale SIC_8

43. 90 cm Four Crescents The diagram shows a circle, four semi- circular arcs and a rectangle (with dimensions given). What is the total area of the four shaded crescents? 10 cm NOT to scale SIC_8