© Nuffield Foundation 2011 Free-Standing Mathematics Activity Perimeter and area

© Nuffield Foundation 2011 The gardener needs to work out the perimeter and the area of the lawn How much edging do I need to go around the lawn? How much lawn feed do I need?

© Nuffield Foundation 2011 Perimeter of a rectangle length width length width = length + width + length + width Think about Is there another way to find the perimeter? Think about Is there another way to find the perimeter? lawn 5 m 3 m = Perimeter of this lawn = 16 m The perimeter of a shape is the total length of its sides

© Nuffield Foundation 2011 Area Area measures the surface of something 1 metre 1 square metre 1 m 2 1 cm 1 cm 2 1 mm 1 mm 2

© Nuffield Foundation 2011 Area of a rectangular lawn 15 square metres The area is 5 metres long 3 metres wide Area of a rectangle= length × width = 15 m 2

© Nuffield Foundation 2011 page 21 cm 30 cm = 30 × 21 Area of the page = m 32 m = 65 × 32 Area of field = 2080 cm 2 Area of rectangle = length × width m2m2 field

© Nuffield Foundation m 4.5 m 3 m 1.5 m 2.2 m To find the perimeter of this L-shaped room Perimeter = 19.4 m Think about What else is needed? Think about What else is needed?

© Nuffield Foundation m 4.5 m 3 m 1.5 m 2.2 m A B Area of A= 4.5 × 3 = 13.5 m 2 Area of B = 3 × 2.2 = 6.6 m 2 Total area = = 20.1 m 2 Think about How can we do this? Think about How can we do this? To find the area of this L-shaped room

© Nuffield Foundation m 4.5 m 3 m 1.5 m 2.2 m A B Another way Area of A = 3 × 1.5 = 4.5 m 2 Area of B = 5.2 × 3 = 15.6 m 2 Total area = = 20.1 m 2 To find the area of this L-shaped room

© Nuffield Foundation m 4.5 m 3 m 1.5 m 2.2 m Yet another way! Area of large rectangle = 5.2 × 4.5 = 23.4 m 2 Area of small rectangle = 2.2 × 1.5 = 3.3 m 2 Total area = 23.4 − 3.3 = 20.1 m 2 Think about Which way was best? Think about Which way was best? To find the area of this L-shaped room

© Nuffield Foundation 2011 What does the word ‘perimeter’ mean? At the end of the activity 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? Car park Play area Carpet Mirror surround