Four Crescents Whats the area of the four

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

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

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? –

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.

Let’s look at the general case.

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

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

Final thought

Resources Surds •

Resources Surds •

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Resources 900 •

Originals

Originals

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

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

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

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

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

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

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

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

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

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

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

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

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

Vanilla Almond Crescents Vanilkov Mandlove Rohlicky Typical CzechVanilla Almond Crescents Vanilkov Mandlove Rohlicky Typical Czech
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