Four Crescents Whats the area of the four

Four Crescents The diagram shows a circle, four semicircular arcs and a rectangle (with

Four Crescents • Compare your answers with others – What do you notice? –

So, the area of the four crescents is the same as the area of

Four Crescents NOT to scale The diagram shows a circle, four semicircular arcs and

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

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

Four Crescents • 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. 5 cm x 4 cm, 16 cm x 7 cm, anything you like – What do you notice now? • Can you prove your assertions?

Let’s look at the general case.

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

Final thought

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SIC_8

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Originals

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

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

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

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

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

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

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

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

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

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

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

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