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

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© 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?

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© 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 = 5 + 3 + 5 + 3 Perimeter of this lawn = 16 m The perimeter of a shape is the total length of its sides

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© 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

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© 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

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© Nuffield Foundation 2011 page 21 cm 30 cm = 30 × 21 Area of the page = 630 65 m 32 m = 65 × 32 Area of field = 2080 cm 2 Area of rectangle = length × width m2m2 field

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© Nuffield Foundation 2011 5.2 m 4.5 m 3 m 1.5 m 2.2 m To find the perimeter of this L-shaped room Perimeter 3+ 1.5+ 2.2+ 3 + 5.2+ 4.5= 19.4 m Think about What else is needed? Think about What else is needed?

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© Nuffield Foundation 2011 5.2 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 =13.5+ 6.6= 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

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© Nuffield Foundation 2011 5.2 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 =4.5+ 15.6= 20.1 m 2 To find the area of this L-shaped room

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© Nuffield Foundation 2011 5.2 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

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© 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

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1.3 Using Formulas Geometry Perimeter Measures the distance around the edge of any flat object. To find the perimeter of any figure, ADD the lengths.

1.3 Using Formulas Geometry Perimeter Measures the distance around the edge of any flat object. To find the perimeter of any figure, ADD the lengths.

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