Starter Which of these shapes has the greatest perimeter?

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Presentation transcript:

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

Answers Square has 4 sides of length d 4d Hexagon has 6 sides of ½d 3d

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

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

Area Large square is 2r x 2r = 4r2 Small square is half of this = 2r2

Area Large square is 2r x 2r = 4r2 Small square is half of this = 2r2 Circle has area in between 2r2 and 4r2

Circles A circle has radius r.

Circles Rearrange the sectors.

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

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

Circles Consider the area. r πr Area of shape is close to area of parallelogram = base x height = πr x r = πr2 Hence the area of a circle is = πr2

Circles A circle has radius r and diameter d. Circumference of a circle C = πd Area of a circle A = πr2

Calculate the area and perimeter of the following shapes: r = 6cm r = 7cm d = 4cm r = 4cm r = 1.5cm 1/8 r = 4cm r = 2cm r = 6cm 60° r = 3cm 45° 165° r = 3cm r = 8cm 225° r = 5cm

Answers A = 6.28cm² A = 14.14cm² A = 12.57cm² A = 38.48cm² P = 10.28cm P = 15.42cm P = 14.28cm P = 25.00cm A = 28.27cm² A = 37.70cm² A = 3.53cm² A = 1.57cm² P = 21.42cm P = 26.85cm P = 7.71cm P = 5.57cm A = 3.53cm² A = 33.51cm² A = 17.67cm² A = 36.00cm² P = 8.36cm P = 24.38cm P = 17.78cm P = 24.40cm

Calculate the area and perimeter of this compound shape: 8cm 12cm

Calculate the area and perimeter of this compound shape: 8cm Area of rectangle = b x h 12cm Area of rectangle = 8 x 12 96cm² Area of rectangle = 96cm²

Calculate the area and perimeter of this compound shape: 56.55cm² 8cm Area of semi-circle = π x r² ÷ 2 12cm Area of semi-circle = π x 6²÷ 2 96cm² Area of semi-circle = 56.55cm²

Calculate the area and perimeter of this compound shape: 56.55cm² 8cm Area of semi-circle = π x r² ÷ 2 12cm Area of semi-circle = π x 4²÷ 2 96cm² Area of semi-circle = 25.13cm² 25.13cm²

Calculate the area and perimeter of this compound shape: 56.55cm² 8cm Total area = 12cm 96 + 56.55 + 25.13 = 96cm² 177.68cm² 25.13cm²