Area of a Circle Starter Which of these

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 • Hexagon has 6 sides of ½d d d ½ d 4 d 3 d d

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

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

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

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

Area of a circle • A circle has radius r

Rearrange the sectors

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

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

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

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