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Free-Standing Mathematics Activity Perimeter and area © Nuffield Foundation 2011 How much lawn feed do I need? How much edging do I need to go around the lawn? © Nuffield Foundation 2011 The gardener needs to work out the perimeter and the area of the lawn The perimeter of a shape is the total length of its sides length Perimeter of a rectangle = length + width + length + width width length 5m lawn width 3m Perimeter of this lawn = 5 + 3 + 5 + 3 = 16 m Think about Is there another way to find the perimeter? © Nuffield Foundation 2011 Area Area measures the surface of something 1 metre 1 cm 1 m2 1 metre 1 square metre © Nuffield Foundation 2011 1 cm 1 cm2 1 mm 1 mm 1 mm2 Area of a rectangular lawn 5 metres long 3 metres wide The area is 15 square metres = 15 m2 Area of a rectangle = length × width © Nuffield Foundation 2011 Area of rectangle = length × width 65 m 32 m field Area of field = 65 × 32 = 2080 m2 21 cm page © Nuffield Foundation 2011 30 cm Area of the page = 30 × 21 = 630 cm2 To find the perimeter of this L-shaped room Think about What else is needed? 3m 1.5 m 4.5 m 2.2 m 3m Perimeter 3 + 1.5 + 2.2 + 3 + 5.2 + 4.5 = 19.4 m 5.2 m © Nuffield Foundation 2011 To find the area of this L-shaped room Think about How can we do this? 3m 1.5 m 4.5 m 2.2 m A B 5.2 m 3m Area of A = 4.5 × 3 = 13.5 m2 Area of B = 3 × 2.2 = 6.6 m2 Total area = 13.5 + 6.6 = 20.1 m2 © Nuffield Foundation 2011 To find the area of this L-shaped room Another way 3m A 1.5 m 4.5 m Area of A = 3 × 1.5 = 4.5 m2 2.2 m B 3m Area of B = 5.2 × 3 5.2 m Total area = 4.5 + 15.6 = 20.1 m2 © Nuffield Foundation 2011 = 15.6 m2 To find the area of this L-shaped room Yet another way! 3m Area of large rectangle = 5.2 × 4.5 1.5 m 4.5 m 2.2 m = 23.4 m2 3m Area of small rectangle = 2.2 × 1.5 5.2 m Total area = 23.4 − 3.3 = 20.1 m2 © Nuffield Foundation 2011 = 3.3 m2 Think about Which way was best? At the end of the activity • • • • • What does the word ‘perimeter’ mean? How do you find the perimeter of a shape? What units are used for perimeters? How do you find the area of a shape? What units are used for areas? • How would you find the area of this shape? © Nuffield Foundation 2011 Car park Play area Carpet Mirror surround