Build your skills: Perimeter and area Part 1. Working out the perimeter and area of different shapes


 Elmer Riley
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1 Working out the perimeter and area of different shapes This task has two parts. Part 1 In this part, you can brush up your skills and find out about perimeter and area. Part 2 In the second part, you can try out these skills on testtype questions. In this task you can find out: what is meant by perimeter and area MSS1/L1.8 MSS1/L1.9 what units to use to measure perimeter and area how to work out perimeter and area of different shapes. Think about how you would measure at home: the distance around the boundary of your garden for a new fence the distance around the edge of your lounge to replace the skirting boards the size of your hall walls to put up wallpaper the size of your porch for a new doormat. 1 Numeracy at Level 1
2 A number of questions within the National Tests in numeracy at Level 1 ask you to work out perimeter and area. The two questions below are examples of ones where knowing how to work out perimeter and area will help you get to the right answer. 1 How long would a fence need to be in order to enclose this plot of land? A 50 metres B 60 metres C 80 metres D 100 metres Scale 1 cm : 5 m The answer is A. (Taken from Progress Check G, question 25.) 2 Another area is paved for the barbecue. The area for the barbecue is: A 3.25 m² B 3.50 m² C 3.75 m² D 4.00 m² The answer is C. (Taken from Progress Check A, question 24.) 2 Numeracy at Level 1
3 What is perimeter? The perimeter of any flat shape is the distance all the way around its edges or outside, for example the distance around the perimeter fence of a football pitch or around the edge of a book cover. It is measured in units such as metres (m) or centimetres (cm) or millimetres (mm), depending on the size of the shape. Perimeter What is area? The area of any shape is the size of the flat space, for example the size of a football pitch or a book cover. It is measured in units such as metres squared (m²) or centimetres squared (cm²) or millimetres squared (mm²), depending on the size of the shape. 3 Numeracy at Level 1
4 Which unit of measurement should I use? Which unit of measurement would you use to measure: a sports hall floor? a shelf? a matchbox top? The unit you use to measure perimeter or area will depend on the size of the surface you are measuring. For example, a sports hall floor is large so you would use metres to measure this. However, a shelf is much smaller, so you would use centimetres to measure this. You would only use millimetres for small shapes, such as the size of small storage boxes on a shelf. 4 Numeracy at Level 1
5 You can use metres, centimetres or millimetres for measuring anything, but you will find it easier to use bigger units of measurement for bigger shapes and you must remember to use the same unit of measurement for measuring the whole shape or object. Don t forget that you can always convert, or swap, between measurements before or after you ve done your calculations. 10 mm = 1 cm 100 cm = 1 m For example, if a table top has a perimeter of 200 cm, you could write this as 200 cm, or convert the figure to 2 m. How to work out perimeter One way to work out the perimeter of a shape is to add together the measurements of all the sides. Look at the picture of the top of a storage box below. To work out the perimeter, add the length of the four sides together: 10 cm + 3 cm + 10 cm + 3 cm = 26 cm This method works with any shape with straight sides. Look at the image of a grass area below: To work out the perimeter, add the length of the four sides together: 5 m m m + 4 m = 18 m 5 Numeracy at Level 1
6 There are quicker ways of working out the perimeter of rectangles. A rectangle is a shape with four sides where the two lengths are of the same size and the two widths are of the same size. Look again at this shape: The longer sides (length) are both 10 cm. The shorter sides (width) are both 3 cm. Note that sometimes the width is called the breadth. These are different words for the same thing, so you can use whichever word you prefer. Quick way 1 The length is 10 cm and the width is 3 cm. The perimeter of a rectangle has two lengths and two widths so: 10 cm 2 = 20 cm 3 cm 2 = 6 cm 20 cm + 6 cm = 26 cm Quick way 2 One length is 10 cm and one width is 3 cm. 10 cm + 3 cm = 13 cm You have two lengths and two widths, so: 13 cm 2 = 26 cm 6 Numeracy at Level 1
7 Activity 1: Have a go yourself What is the perimeter of these shapes? Note that none of the shapes are drawn to scale. 1 This bedroom: 2 This courtyard: 3 This garden: 7 Numeracy at Level 1
8 How to work out area Remember that the area of any shape is the size of the flat space, for example the size of a football pitch or a book cover. The way to work out the area of a shape is to multiply the length by the width. Using the same example as above, the area of this rectangle below would be: 10 cm 3 cm = 30 cm² Note that the measurement for area is always written as squared, e.g. 30 cm². This is because the area is made up of lots of individual squares. Look at the grid below. If you count up the number of squares, you will find there are 30 squares, which is the same answer you get if you multiply the length and width together. 8 Numeracy at Level 1
9 Activity 2: Have a go yourself What is the area of these shapes? Note that none of the shapes are drawn to scale. 1 This living room: 2 This bathroom tile: 3 This garden: 9 Numeracy at Level 1
10 Now you can use these skills to solve some practical problems. The following activities are based on working in an afterschool club. Activity 3 You need to work out how much edging to buy to put around the edge of the sandpit in the playground. The sandpit is a rectangle and has a length of 180 cm and a width of 140 cm. a b How much edging do you need? What is the area of the sandpit in metres? Activity 4 You are putting up a new noticeboard for parents in the entrance hall. You want to decorate the edge of the board with ribbon and put coloured paper on the noticeboard to make it more cheerful. The noticeboard is 60 cm long and 30 cm wide. a b How much ribbon will you need to go all the way around the edge of the noticeboard? How much coloured paper will you need to cover the noticeboard? 10 Numeracy at Level 1
11 Activity 5 The kitchen of the afterschool club needs new vinyl flooring. The kitchen floor is a square and each side is 4.5 metres. You can only buy vinyl flooring by the full metre, so you may have to buy more than you need. How many square metres of vinyl flooring do you need to buy? Now print out Part 2 to try out your skills further and check your answers. 11 Numeracy at Level 1
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