# Area of a Circle π. Starter Which of these shapes has the greatest perimeter? Which has the smallest? What is each perimeter in terms of d? d d d.

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Area of a Circle π

Starter Which of these shapes has the greatest perimeter? Which has the smallest? What is each perimeter in terms of d? d d d

Starter Answer Square has 4 sides of length d 4d Hexagon has 6 sides of ½d3d d d d ½d

Starter Answer Square has 4 sides of length d 4d Hexagon has 6 sides of ½d3d Circle is between 3d and 4dπd

Areas Which of these shapes has the greatest area? Which has the smallest? What is the area in terms of r? rrr

Areas Large square is 2r x 2r = 4r 2 Small square is half of this = 2r 2 rrr 2r

Areas Large square is 2r x 2r = 4r 2 Small square is half of this = 2r 2 Circle has area in between 2r 2 and 4r 2

Area of a circle A circle has radius r

Rearrange the sectors

Consider the lengths Circumference of circle = 2πr Length of half circumference = πr So the length of this side is πr

Consider the lengths Radius of circle = r So the height is r πrπr

Consider the area Area of shape is close to area of parallelogram = base x height = πr x r = πr 2 r πrπr Hence the area of a circle is = πr 2

Summary A circle has radius r and diameter d Circumference of a circle C = π d or C = 2 π r Area of a circle A = π r 2 r d Fiddle-dee-dum, fiddle-dee-dee A ring round the moon is π times d But if you want a hole repaired Then what you need is πr 2.

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